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U. S. MILITARY ACAOeivlV. 



COURSE OF INSTRUCTION 



IN 



ORDNANCE AND GUNNERY 



TEXT. 



BY- 



Captain HENRY METCALFE, 

Ordnance Dep't, U. S. Army, 

Instructor of Ordnance and G winery, U. S. Military Academy. 



SKCOND KDITION. 



^^ OP TEra"^^ 

UHiyERSITY] 

*^^^ — 1891. 






Copyright, 1891, 

BY 

Henry Metcalfe. 



CONTENTS 



CHAPTER 


I. 


CHAPTER 


II. 


CHAPTER 


III. 


CHAPTER 


IV. 


CHAPTER 


V. 


CHAPTER 


VI.- 


CHAPTER 


VII.- 


CHAPTER 


VIII. 


CHAPTER 


IX.- 


CHAPTER 


X. 


CHAPTER 


XI.- 


CHAPTER 


XII.- 


CHAPTER 


XIII.- 


CHAPTER 


XIV.- 


CHAPTER 


XV. 


CHAPTER 


XVI.- 


CHAPTER 


XVII.- 


CHAPTER 


XVIIL- 


CHAPTER 


XIX.- 


CHAPTER 


XX.- 


CHAPTER 


XXI.- 


CHAPTER 


XXII.- 


CHAPTER 


XXIII.- 


CHAPTER 


XXIV.- 


CHAPTER 


XXV.- 


CHAPTER 


XXVI.- 


CHAPTER 


XXVII.- 


CHAPTER : 


XXVIII.- 


CHAPTER 


XXIX.- 


CHAPTER 


XXX.- 



-Definitions. ) 

-Explosive Agents. 

-Ingredients of Gunpowder. , 

-Manufacture of Gunpowder. J 

-Interior Ballistics. 

-Velocimeters. 

-Pressure Gauges. 

-Phenomena of Conversion. 

-Noble and Abel's Experiments. 

-Combustion of Gunpowder in the Air. 

-Combustion of Gunpowder in the Gun. 

-Sarrau's Formula for Interior Ballistics. 

-History of Gunpowder. 

-High Explosives. - / 

-Metallurgy. 

-Projectiles and Armor. 

-Manufacture of Projectiles. 

-Means of Communicating Fire. 

-Gun Construction. 

-Exterior Ballistics. 

-Varieties of Cannon. 

-Artillery Carriages, Principles. 

-Various Artillery Carriages. 

-Horse and Harness. 

-Artillery Machines. 

-Hand Arms. - { 

-Small Arm Ammunition. 

-Small Arms. '- 1 

-Cannon Without Recoil. 

-Accuracy of Fire. 



PREFACE TO SECOND EDITION, 



The great advances which have been recently made in our 
knowledge of the properties of gunpowder have subjugated 
the " Spirit of Artillery," as this agent has been termed, to a 
seemingly docile servitude. These, with corresponding 
improvements in Metallurgy, have led to such changes in 
nearly all that relates to fire-arms as to make necessary 
a comprehensive revision of the course of Ordnance and 
Gunnery, established by the late Colonel James G. Benton 
in 1861, and modified from time to time by his successors on 
the Academic Board. 

The subject has outgrown the limits of the small encyclo- 
pedia in which Benton comprised all that was then essential 
for the ordinary officer, as well as for the student, to know of 
the materiel of war. 

It has also lost much of the stability which characterized 
it when spherical projectiles were still generally employed. 
The labors of men of science and the energy of inventors 
are continually extending the boundaries of knowledge and 
undermining positions which appear most fixed. 

Therefore, instead of giving to the course a descriptiv^e 
character, it appears advisable to frame it so as to present 
as simply as possible such of its principles as are the most 
important, and appear the best established. 

By employing the short time available for this course in 
teaching such principles, the student, although less familar 
with existing forms and methods than after the study of the 
former course, may possibly be better fitted to understand 
the causes of changes in materiel which are now so frequent, 
and, as his experience increases, to wisely advise the direc- 
tion that such changes should take. 



VI PREFACE. 



The selection, enunciation and deduction of such princi- 
ples in a suitable form is rather embarrassed than assisted 
by the mass of specialized knowledge to be found in the 
Government reports and in the periodical press. In fact, 
had it not been for the admirable text-books used at the 
^'''Ecole d'' Application de VArtillerie et du Genie^'' at Fontaine- 
bleau, France, for a set of which the author is obliged to 
superior military and diplomatic authority, it would not 
have been possible for him to prepare many of the following 
pages. 

Graphical methods have been freely used, both to express 
abstract relations and to avoid description. In order to 
reheve the memory and to train the student in reading 
mechanical drawings, it is intended that the more elaborate 
shall be recited on from the book. 

It has been attempted to give the antecedents of present 
forms, briefly, but so as to indicate the general lines fol- 
lowed in their evolution and possibly to anticipate the 
direction in which their improvement tends. In so doing 
more stress than heretofore has been laid upon the practice 
of the workshops; since the history of invention shows 
that this has had as much to do with the march of improve- 
ment as a special knowledge of the military necessities of 
any particular case. 

The thanks of the author are due : 

To Mr. Geo. H. Chase, of the Midvale Steel Works, Phila- 
delphia, for revising Chapter XV. 

To Captain Z. L. Bruff, Ordnance Department, for the 
appendix to Chapter XIX, relating to the Elastic Strength 
of Guns. 

To Private C. August Schopper, of his detachment, for 
most of the drawings used in illustration. 

West Point, New York, yuly 1, 1891. 

HENRY METCALFE, 



Bibliography of the Principal Works Consulted. 



Benton's Ordnance and Gunnery. 6th Edition. 

Mordecai's Revision of Benton. Pamphlets, U. S. M. A. 

McKinlay's Text-Book of Gunnery. British. 1887. 

Cooke's Naval Ordnance and Gunnery. 2nd Edition. 

Text Book of Ordnance and Gunnery, U. S. N, A. 1887 

Noble and Abel's Experiments on Fired Gunpowder. 2 Vols, 1880. 

Proceedings U. S. Naval Insiitute. Current series. 

Encyclopedia Brittanica. 9th Edition. 

Bloxam's Chemistry. 6th Edition. 

Byrne's Metal Worker's Assistant. 1869. 

Goodeve's Principles of Mechanism. 1876. 

Reports of the Chief of Ordnance, U. S, A. 1872 — 1890. 

Ordnance Notes, U. S. A. 

Notes on the Construction of Ordnance, U. S. A. Current series. 

Reports on Naval Progress, U. S. N. 1887 — 1890. 

Principal French Works. 
Roulin's. Poudres de Guerre et Balistique Int^rieure. 1884. 

do Armes Portatives. 1885. 

Pi^bourg. Fabrication de la Poudre. 1884. 

do Pyrotechnic. 1884. 

Jouffret. Les Projectiles. 1881. 
Berthelot. Sur la force de la Poudre. 1872. 
Muzeau. Effets du tir sur les affuts. 1884. 
Bornecque. Armes ^ repetition. 1888. 
Malengrau. L'Artillerie a I'Exposition. 1890. 
Aide Memoire. Artillerie. 1887. 

Referritig to Chapter XII. 
Meig's and Ingersoll's Interior Ballistics, U. S. N. A. 1887. 
Medcalfe and Howard. Notes on Construction of Ordnance. N0S.36&42. 
The above are derived principally from Sarrau's ** Researches on the 
Effect of Powder," translated in the Proceedings of the U. S. Naval 
Institute. Vol. X. Whole No. 28. And from ** Researches on the 
Loading of Fire Arms." 1882. 



VIU BIBLIOGRAPHY OF THE PRINCIPAL WORKS CoNStJLtED. 



Referring to Chapter XIV. 
Abbott's Submarine Mines. i88i. Appendices. 
Eissler's High Explosives. 1884. 
Monroe's Notes on Explosives. 1888. 

Referring to Chapter XV. 
Greenwood's Steel and Iron. 1884. 
Bauerman's Metallurgy of Iron. 1868. 
Jean's Steel, History, Manufacture, etc. 1880. 
Thurston's Text-Book of Materials of Construction. 1886. 
Chernoff on the Structure of Steel. Note on Construction of Ordnance. 

No. 22. 
Brinell on the Structure of Steel. Note on the Construction of Ordnance. 

No. 37. 

Referring to Chapter XVI. 
Proceedings U. S. Naval Institute. No. 56. 1890. 
Ordnance Construction Notes, 28, 49. 

Referring to Chapter XVII. 
Ordnance Construction Note, 26. 

Refe'^ring to Chapter XIX. 
Ordnance Construction Notes, 9, 19. 

Referring to Chapter XX. 
Bruff 's Ballistics. 1885. 
Ingalls' Exterior Ballistics. 1886. 

Referring to Chapter XXX. 
Glennon's Accuracy and Probability of Fire. 1888. 



REMARK. — The unusual method of paging adopted in this work is 
intended to facilitate its revision, since new chapters can be inserted with- 
out disturbing the sequence of the following pages. 



INDEX 



The heavy figures refer to the number of the chapter, and the lighter 
figures to that of the page. 



Abbott's experiments, 14, 1. 

Abbreviations, 1, 4. 

Abel, gun cotton, 14, 10. 

Absolute error, 30, '24; force of 

gunpowder, 9, 6. 

Accidents, fuzes, 18, 19; gunpow- 
der, 4, 1; high explosives, 

14, 1. 

Accles feed, 29, 6. 

Accuracy of lire, 30, 5; estimated, 

30, 23, 35. 

Acoustic telemeters, 30, 11. 

Air, combustion in, 8, 2, 10, 3, 4, 12, 
3; packing, 7, 4, 21 , 7; re- 
sistance of, 16, 1, 20, 8; spac- 
ing, 11, 14; trajectory in, 20, 

18. 

Aluminium in steel, 15, 20. 

Ammonium nitrate, 3, 7. 

Ammunition and arms, relation, 27, 
1; chest, 22, 28; rapid fire, 

29, 18, 20; small arm, 27, 9, 

28, 19; supply of, 2S, 17. 

Ancient cannon, 13, 1; carriages, 

i8l, 20; gunpowder, 13, 2. 

Analysis of gunpowder, 2, 10, 9, 2, 
11, 29. 

Angle of fall, 20, 37, 30, 35; of 

draught, 24, 3. 

Animal power, 24, 1, 3, 28, 2. 

Animate objects, 10, 23; areas, 

30, 48. 

Annapolis armor tests, 16, 43. 

Annealability, 15, 23. 

Annealing, 15, 38, 51, 52, 57; vrater, 

15,54. 
Anvils, forging, 15, 44. 46; for 

])rimers, 27, 4. 



Armor, kinds of, 16, 36; piercing 

shell, 16, 20, 29, 21; penetration 

of, 16, 36; test for projectiles, 

17. 18. 

Arms and ammunition, relation, 27, 1. 

Artillery carriages, 22, 1; system 

of, a 1,3. 

Assembling cannon, 16, 58. 

Axle, 22, 24. 

B. 

Back gear, 17, 12. 

Backing, armor, 16, 37. 

Back rest, 17, 13. 

IJallistics, interior, 5, 1; exterior, 

20, 1; coefficient (gunpowder) 

12, 13, 28. 21; projectile, 

16, 2, 20, 11, 23; formulae, 20, 

28, 47; tables, 20, 27. 53. 

Balloting of projectile, 16, 15. 

Bands, carrying, 4, 5; rotating, 

16, 12, 15, 17,2,15. 

Barbette carriage, 22, 2, 23, 5. 

Harlow's law, 19, J, 4. 

Barrels, mixing, 4, 5; tumbling, 

4, 4; small arm, 28, 2. 

Bashforth, experiments, 20, 9; 

target, 6, 15 

Basic process. 15, 19, 35, 37. 

Batteries, electric, 6, 15, 18, 5. 

Bayonet, 26, 1. 

Beaten zone, 30, 49. 

Belleville springs, 22, 19, 23, 4. 

Bellite, 14, 16. 

Belts, 17, 12. 

Benton velocimeter, 6, 3. 

Berdan telemeter, 30, 15; primer, 

27,4. 

Berihelot's theory, explosives, 2, 3. 

Bessemer process, 15, 32, 35 j »»« 



ind: X. 



Bickford fuze, 18, 2. 

Blacking arms, aS, 29. 

lilack wash, l"?, 3. 

Blasts, size of, 14, 2. 

Blasting fuze, 18, 2; powder, 8, 

7, 9, 9, 2. 
Blending gunpowder, 4, 13. 
Blister steel, 15, 14, 30. 
Blooms, 15, 43. 
Blow holes, 15, 21. 
l?o]t guns, 88, a. 
Bomford's experiment, 7, 15. 

Bore, rocket, 16, 44; and parts 1, 1. 

Boring, 17, 13. 

Bormann fuze, 18, 9. 

Boxer shrapnel, 16, 31, 32. 

Box magazines, 88, 11. 

Brakes, 22, 11, 18. 

Brinell's experiments, 15, 49. 

Brgger's chronograph, 6, 10. 

Breaching, 14, 19, 16, 20. 

Breech, 1, 2. 

Breeching, 24, 7. 

Breech loading, advantages of, II, 16, 

13, 2, 28, 1; projectiles, 

5, 3, 16, 14; small arms, 

28,5. 
Broad well ring, 21, 7. 
Bronze, 15, 14, 20, 24, 19, 12; 

quenched, 15, 22. 
Browning arms, 28, 29. 
Blown powder. ( See Cocoa.) 
Bruce feed, 29, 5. 
Brug^re powder, 1 4, 18. 
Buffers, 23, 14. 
Buffington brake, 22, 19, 23, 2; 

carriage, 23, 1. 
Built up guns, 19, 12,22. 
Bullet, manufacture, 27, 8; small 

caliber, 28, 2, 20. 
Burden of ammunition, 28, 4, 28, 18 
Bursting charges, 14, 7, 19, 16, 20, 26, 

32, 19, 17, 29, 17. 
Butler projectile, 16, 13. 
Buttofrifle, 28, 3. 



C. 



Caisson, 22, 29, 23, 2. 
Cake powder, 13, i, 



Caking, 16, 20. 

Caliber, 1, 1; influence of, 16, 7, 

17; small arm, 28, 2. 

Canet system, 21, 13. 

Canister, 16, 23, 25, 28, 82, 28. 

Cannelures, 27, 8. 

Cannon, 1, 1; B. L., 5, 3, 13, 2; 

construction of, 19, 1, 22; 

dimensions of, 13, 25, 21, 22; 

disabling, 14, 20; metals, 15, 

13, 24; M. L , 6, 3, 13, 2, 21, 

4; nomenclature, 1, 1; 

proportions of, 5, 2, 19, 46; 

varieties of, 21, 1. 

Carbine, 28, 1. 

Carbo-hydrates, 11, 28. 

Carbon, cement, 15, 18, 48; hard- 
ening, 15, 18, 48; states of, 15, 

48; in steel, 15, 18. 

Carbonizers, 15, 28, 32, 36. 

Carcass, 16, 22. 

Carriages, artillery, 22, 1. 

Cartridge, anvil, 27, 4, 5; cor- 
roded, 27, 6; limit of size, 29, 

IS; manufacture of, 27, 6; 

metals, 27, 5; origin, 87, 1; 

resizing, 27, 6, 

Case hardening, 15, 27. 

Case shot, 16, 18, 23. 

Castan's powder, 4, 12. 

Casting, 17, 1; cannon, 15, 58, 19, 

12; ingots, 15, 33, 56; steel, 

15, 42. 

Cast iron, 15, 24; projectiles, 

16, 5, 6. 

Cavity in shells, 16, 18, 22. 

Cellular theory, 15, 21. 

Cement carbon, 15, 18, 48. 

Center of impact, 30, 23; marks, 

17, 13. 

Centering projectile, 16, 12. 

Central fire cartridge, 27, 4. 

Chamber, 1, 1, 5, 3. 

Change gear, 17, 12. 

Charcoal, brown, 3, 5, 4, 14, 11, 28 ; 
material, etc., 3, 1; pre- 
paration, 3, 2; properties, 3, 

4; — spontaneous ignition, 3, 4. 

Cbase, 1, 3r 



INDEX. 



Chassis, 32, 2. 

Chauvenet's table, 30, 36. 

Chest, ammunition, 32, 28. 

Chi (x), coefficient, 11, 20, 13, 28; 

factors of, 13, 29; maximum 

value of, 13, 31. 
Chilled iron, 16, 5, 17, 6, 9, 14. 
Chlorates, 3, 7, 14, 19. 
Choice of formulae, Sarrau, 13, 6. 
Chromium in steel, 15, 20. 
Chronograph, Le Bouleng6, 6, 6. 
Chronoscope, 6, 13. 
Chuck, lathe, 17, 13. 
Clips, 33, 9, 33, 6 
Cluster, 16, 23. 
Cocoa powder, manufacture, 4, 13 ; 

theory, 11, 27. 

Coefficient, ballistic, 13, 13, 16, •?, 30, 

11, 23 ; of efficiency, 30, 52 ; 

of elasticity, 16, 4, 10, 19,9, 

22; internal ballistic, various, 

11, 19; Wertheims, 19, 2, 3, 25. 

Cold and heat, on high explosives, 

14, 6; rolling, 15, 24, 42; 

shuts, 15,44. 
Collective fire, 30, 48. 
Combination fuze, 18, 6, 15. 
Combustion, condition of, 3, 4; in 

air, 8, 2, 10, 1; in gun, 8, 2, 

11, 1, 4; rates, 8, 2, JO, 3, 13, 

3; volume, 11, 1. 

Commercial values, 3, 9, 14, 2, 31, fi. 
Common properties, high explosives, 

14,2. 
Communicating fire, 18, 1. 
Component parts of arms, 38, 2; 

of ammunition, 37, 8. 
Composition of gunpowder, 3, 10, 9, 2. 
Compound cylinder, strength of, 19, 

14, 33. 
Compressive projectiles, 5, 3, 16, 14. 
Concrete powder, 4. 11. 
Concussion fuze, 18, 11. 
Condie's hammer, 15, 46. 
Conditions of loading, 13, 16. 
Cone of dispersion, 16, 23, 26, 30, 49; 

pulley, 17, 11. 

Constants, physical, 34, 2, 38, 16; 



Constitution of steel, 15, 16. 
Converted guns, II, 21, 19, 8, 31, 3, 

5, 38, 15, 
Conversion of gunpowder, 3, 1; 

rate of 8, 3, 10, 2, 13, 3; phe- 
nomena of, 8, 1. 
Cooling, 15, 21, 49. 
Cope, 17, 5. 
Cores, 17, 4, 8, 11. 
Coring, 15, 56. 
Corning mill, 4, 11, 13. 3. 
Counter recoil, 33, 18; shaft, 17, 

12 
Cradle, 35, 2. 
Cranes, 1 5, 33, 

Crank axle, 33, 29; kinds of, 39, 7. 

Crozier's deduction, 19, 27; gun, 

19, 18. 
Crucible steel, 15, 31. 
Crusher gauge, 7, 4. 
Crystallization, 15, 21. 
Cube, elastic, equilibrium, 19, 25. 
Cubic law, 30, 12, 16. 
Cup-anvil, 37, 4. 
Cupola furnace, 15, 25. 
Curvature of cutting arms, 36, 3. 

Cutting arms, 36, 2; speed, 17, 12. 

Cut-ofl", 38, 11. * 

Cylinder, elastic, equilibrium, 19, 26, 

31; gauge, 17, 17; strength 

of, 16, 19, 19, 6, 31, 33. 



Damascus steel, 15, 55. 

Dangerous fragment, 16, 19 ; 

space, 1, 3, 30, 39, 43, 49, 38, 4 ; 

zone, 30, 49. 

Dank's furnace, 15, 29. 

De Bange gas check, 31, 8. 

Definitions, general, 1, 1. 

Deformation, process of, 7, 3. 

Delayed action fuze, 18, 19. 

De Marre, formula for armor, 16,40. 

Demolition, 14, 19. 

Density, gravimetric, 9, 3 ; of 

loading, 9, 4, 12, 11, 14, 13, 1; 

sectional, 16,1; — spherical, 16,6. 
Departure, angle of, 30, 2, 45j -i— ™» 

liue Of, 20, 1, 



INDEX. 



Depression range finder, 30, 14. 

DesignoUe powder, 1*, 17. 

Detachable magazine, 38, 11. 

Detonation, 2, 3, 4, 14, 3; sympa- 
thetic, 8, 5. 

Detonator, 3, 5, 14, 3, 18, 3; tube, 

18,2. 

Development of small arms, 28, 17. 

Deviations, 80, 4, 30, 6, 23; causes 

of, 30, 6. 

Dimensions of cannon, changes in, 
19, 27, 37. 

Dirigibility, 29, 13. 

Disabling cannon, 14, 20. 

Disappearing carriage, 83, 13. 

Dish of wheel, 23, 24. 

Disjunctor, 6, 4, 7. 

Dispart, 1, 2. 

Dissociation, 3, 1. 

Distance, estimation of, 30, 10. , 

Drag, 17, 5. 

Draught, angle of, 34, 3; horse, 

34, 1; of patterns, 17, 4. 

Drawn cartridge, 37, 7. 

Drift, 30, 4, 30, 8. 

Drill cartridge, 39, 20. 

Drop test, 15, 15. 

Drying gunpowder, 4, 12. 

Dog, lathe, ir, 13. 

Ductility, 15, 11. 

Dusting gunpowder, 4, 13. 

Dynamite, 14, 4, 13. 



E. 

Early cannon, 13, 1; carriages, 

31, 20; shrapnel, 16, 30; 

fuzes, 18, 7, 8. 
Eccentric turning, 38, 29. 
Economy, coefficient of, 11, 19. 
Effective work of gunpowder, 11, 11. 
Effect, factor of, 11, 11, 21. 
Efficiency of fire, 30, 52. 
Elasticity, 15, 3, 11; coefficient of, 

15, 4, 19, 22; varying, 19, 9. 

Elastic limit, 15, 4, 19, 22; choice 

of, 19, 33; gtrength of guns. 



Electric batteries, 6, 15, 18, 5; 

primers, 18, 4. 

Electro-welding, 15, 23, 17, 15, 19, 19. 

Elevation, angle of, 30, 1. 

Emergency powder, 8, 4. 

Emmensite, 14, 17. 

Energy, 3, 6, 5, 1, 16, 1, 18, 30, 22; 

of recoil, 19, 19, 33, 4, 38, 16, 39, 

1; of rotation, 16, 3; waste 

of, 9, 10, 11, 8. 

Engelhardt buffer, 33, 18. 

Envelope of cluster, 16, 23; of tra- 
jectory, 30, 6. 

Equilibrium, equations of, 19, 25, 27. 

Erosion of gun, 9, 13, 19, 20. 

Errors, 30, 6, 22, 24. 

Estimation of distances, 30, 10. 

Eta iv), 11, 19. 

Eureka projectile, 16, 14. 

Eprouvette, 7, 2, 9, 5, 13, 3. 

Expanding projectile, 16, 13. 

Expansion volume, 11,1; volumes 

of, 11, 12. 

Experiments, rule for, 9, 1. 

Exterior ballistics, definitions, 30, 1. 

Explosion, 5i, 1; orders of, 3, 2, 4; 

Berthelot's theory, 3, 3; 

temperature of, 9, 8. 

Explosive compounds, J8, 10; 

gelatine, 14, 15; high, 3, 10, 

14, 1; military, 3, 9; mix- 
tures, a, 9; reactions, 3, 3; ^— 

strength of, 2, 6; value of, », 8. 

Eye, error of, 30, 7. 



F. 

Face plate, 1 7, 11. 

Facings, 17, 3. 

Factor of effect, 11, 11, 21. 

Fall, angle of, 30, 37, 30, 35. 

Feed case, 39, 5 ; of machine 

guns, 39, 5, 12; screw, 17, 12. 

Fermeture, cannon, 31, 9, 15; small 

arms, 38, 5. 
Ferreous metals, 15, 13, 24. 
Ferro-manganese, 15, 28j ^UiQOn, 

15,28, 



INDEX. 



Field cannon B L., 21, 17; 

M. L., 81, 4; mortar, 31, 17; 

sight, 30, 3, 

Final velocity, 20, 17. 

Finishing projectiles, 17,10. 

Fire, angle of, 20, 5, 22, 9; arms, 

1, 1; classification of, 20, 5; 

line of, 20, 5; plane of, 

20, 4; works, 14, 1<J. 

Firing, 2, 2; gunpowder, 8, 1; 

high explosives, 14, 3. 

Fiske range finder, 30, 15. 

Fixed carbon, 16, 48; magazines, 

28, 12. 
Flagler fuze, 18, 17. 
Flasks, 17, 5, 8, 22, 3. 
Flatness of trajectory, 1, 3, 20, 23, 

40, 28, 20. 
Flow of metals, 15, 11, 87, 7. 
Folded head, 27,3. 
Follow-board, 17, 5. 
Food and feed of arms, 27, 1, 29, 12. 
Force, 2, 7, 9, 7, 11, 2!), 12, 29, 14, 5. 
Forcite, 14, 14. 
Forging, 15, 45, 53; cannon, 16, 

56; press, 16, 47. 

Fork, establishing, 30, 21. 

Form of cannon, 6, 2, 9, 13, 13, 2, 19, 

6, 46, 21, 1. 
Founding, 17, 1. 
Fractures, 15, 20, 49. 
Free carbon, 15, 48. 
French fuze, 18, 13, 16; system, 

21 , 10. 

Freyi-e gas check, 21, 7. 

Friction checks, 22, 11; clutch, 

22, 12; .primers, 18, 3. 

Fioloir, formula for armor, 16, 38. 
Fulminates, 2, 10, 14, 18. 
Fulmi-bran, 14, 11. 

Functions, ballistic, 20, 27; experi- 
mental, 9, 1, 5; independence 

of, 9, 1, 16, 34, 18, 16, 19, 16, 21, 2, 
19, 22, 22, 23, 24, 6, 26, 3, 4, 27, 4, 
28, 4, 15, 29, 4, 8, 15, 24. 

Fundamental laws, gun construction, 
19, 29. 

Furnaces, 15, 25, 29, 39, 45. 

Fusibility, 15, 22. 

Fusse, principles of, 16, J8, 28, la, 7. 



Gadolin's law, 19, 9, 20,44. 

Gardner gun, 29, 7. 

Gaseous fuel, 16, 38. 

Gas checks, 7, 3, 13, 2, 21, 6. 

Gate, 17, 9. 

Catling gun, 29, 2. 

Gauging, 4, U, 17, 17, 28, 25. 

Gautier range finder, 30, 18, 

General coeflicient, gunpowder, 11, 
20, 12, 28. 

Gerdon fermeture, 21, 15. 

Giant powder, 14, 13. 

Gin, 26, 1. 

Glazing gunpowder, 4, 12. 

Gordon range finder, 30, 20. 

Graining gunpowder, 4, 11, 13, 3. 

Grains, diameter of, 10. 2, 12, 4. 

Granulation of gunpowder, 4, 10. 

Grape shot, 16, 23, 25. 

Gravimetric density, 9, 3. 

Grazed zone, 30, 49. 

Grenades, 16, 20. 

Gribeauval carriage, 32, 25. 

Grinding, 1.5, 21, 17, 14. 

Ground, slope of, 30, 51. 

Guide, rocket, 16, 45. 

Gun, 1, 1; combustion in, 8, 2, 11, 

1, 4; form of, 5, 1; lift, 

25,1. 

Gun construction, theory, 19, 11, 23; 
Itractice, 15, 56. 

Gun cotton, 14, 2, 8 ; detona- 
tion of, 2, 6. 

Gunpowder, adapted to gun, 11, 7, 24, 
12, 16, 32, 13, 3, 6; advan- 
tages of, 2, II; characteristics, 

12, 2, 22; composition of, 2, 10, 

9,2; concrete, 4, 11,16,21; 

fiat, 4, 12, 13, 5; Fossano, 13, 

5; history of, 13, 1; hexag- 
onal, 13, 5; ingredients, 3,1; 

machinery, 4, 2; manu- 

ficture, 4. 1; modern, 13, 6; 

modulus of qaickness, 12, 10, 

29; — pebble, 4, 12, 13,5; pris- 
matic, 4, 15, 10, 4, 11, 6, 13, 4, 6; 
products of, 2, 10, 9. 6, II, 29; 

-^reaction, a, loj — KodmaB's, 



INDEX. 



13, 3; small caliber, «7, 9, 2S, 

21, 22; smokeless, 3, 7, 14, 8, 

15, 88, 22; sphero hexagoual, 

13, 5; work of, 11. 10. 

Gustavus Adolphus, 27, 1. 



Hale rocket, 16, 46. 

Hall rifle, 87, 2. 

Hammers, 15, 45. 

Hand arms, 36, 1 

Hardening, 15, 22, 52; carbon, 15, 

15, 48; strains, 15, 55. 

Harness, 84, 6. 

Heat of gunpowder, ^, 6, 9, 7; 

waste of, 9, 10, 1 1, 8. 
Hebler, system, 88, 19. 
Helhofite, 14,16. 
High explosives, 8, 10, 14, 1; 

for bursting charge, J6, 21; 

use of, 14, 7, 19. 

History of ammunition, 87, 1; 

of gunpowder, 13, 1; of rifling, 

16, 8; of shrapnel, 16, 30; 

of small arms, 87, 1, 88, 1, 16 

Hitting, probability of, 30, 27, 35, 43 

Hollow of wheel, 548, 24. 

Hooke's law, 19, 22. 

Horse and harness, 84, 1. 

Hotchkiss ammunition, 89, 20; 

brake, 88, 12; field carriage, 

89, 20; fuzes, 18, 14; guns. 

81, 16, 17; mounts 89, 1; 

rapid fire gun, 29, 21; revolv- 
ing cannon, 89, 14; projectile, 

16, 15, 17. 

Housing, pressure gauge, 7, 4. 

Howitzer, 1, 1; siege, 81, 18. 

Hydraulic bufier, 88, 14, 83, : ; 

forgingpress, 15, 47; Jack, 85, 

1; motor, 4, 9, 15, 15, 33, 34, 47, 

17, 14. 

Hydro pneumatic carriage, 88, .18. 

Hypothesis, Barlow, 19, 2; Noble's, 

9,8. 

I. 

Ignition of gunpowder, 8, 1; and 

infl^mmAtioa iu guns, 1 1, 18. 



fuze. 



Igniting charges, 18, 5. 
Impact, center of, 30, 23; 

16, 18, 18, 6, 11. 
Immovable layer, 7, 1, 11, 9 
Incendiary projectiles, 16, 22. 
Increasing twist, J6, 9, IJ, 15. 
Incorporation of gunpowder, 4, 7, 16, 

44. 
Independence of function, 9, 1, 16, 

34, 18, 16, 19, 16, 81, 2, 19, 22, 88, 

23, 84, 6, 86. 3, 4, 87, 4, 88, 4, 15, 

89, 4. 8, 15, 24. 
Inertia igniter, 18, 10, 16, 17. 
Inflammation of gunpowder, 8, 1; 

prism, 16, -21. 

Ingots, 15, 34; metals, 15, U. 

Initial tension, 19, 11, 23. 

Initial velocity, 1, 2. 

Inspecting instruments, projectiles, 

17, 17. 
Interchangeability, 88,25. 
Internal strain, 15, 21, 55, 19, 12. 
Interrupted screw, 81, 11. 
Interrupter, 6, 12. 
Interstitial volume, 9, 3. 

Iron castings, 15, 24, 26, 27. 



Judson powder, 14, 14. 
Jump, 80, 2, 3. 



Kalchoids, 15, 14. 

Kinetic measures, 7, 9, 16. 

King carriage, 8Si, 13. 

Krupp fuze, 18, 15; gun, 15, 15, 

81. 6, 9; process, 15, 19; 

steel, 15, 15, 32. 



Lathe, 17, 11; 

13. 
Lance, 86, 1. 
Lands. 1,2. 
Leather, 84, 9. 
Lead, projectiles, 16, 5, 24 
Lead of wheel, 88, 24. 
Lebel powaer, 14, 18. 



variations of, 17, 



INDEX. 



Le Bouleng6 Telemeter, 30, 11; 

chronograph, 6, 6. 
Lee rifle, 38, 7, II. 
Lemoine brake, 33, 19. 
Length of bore, 5, 2, 7, II, 11, IJ, 13, 

2, 19, 47. 
Levers in guns, 27, 6, 28, 6. 
Light balls, 16, 22. 
Limber, 23, 27, 23, 2; chest, 22, 

28 
Limiting values of pressures, 19, 39. 
Line of departure, J*0, 1; of metal, 

1, 2; of signt, ao, 1. 

Liners, 19, 20. 

Liquation, 15, 16. 

Loam, 17, 3. 

Lock, Springfield, 28, 16, 

Longitudinal stress, 19, 16, 30. 

Longridge gun, 19, 19. 



M. 

MacDonald, Hale rocket, 16, 45. 

Machines, artillery, 25, 1; guns, 

21, 1, 29, I, 12. 

Magazine arms, 27, 3, 28, 9, 13, 14. 

Maitland formula for armor, 16, 38. 

Malleability of metals, 15, 23. 

Malleable castings, 15,27. 

Mandreling, 15. 22, 19, 11. 

Mandrels, forging, 15, 47. 

Manganese in steel, 15, 19. 

Mannlicher rifle, 28, 12. 

Manometric balance, 7, 8. 

Manufacture of ammunition, 27, 6; 
of fuzes, 18, IS; of gun- 
powder, 4, 5; of projectiles, 

17, 1; of small arms, 28, 24. 

Marking gunpowder, 4, 13. 

Matches, 18, 1. 

Maxim aut. machine gun, 29, 8; 

rapid fire gun, 29, 25. 

Mayewski's experiment, 7, 9. 

Mean error, 30, 24, 33; point of 

impact, 30, 23; trajectory, 16, 

23, 30, 6. 

Mechanism, small arm, 28, 5. 

Megagraph, 6, 7. 

MeUing^, 15,24, n,6. 



Metals for cartridges, 27, 5; ord- 
nance. 16, 13; physical prop- 
erties of, 15, 13; useful prop- 
erties of, 15, 15. 

Metallic cartridges, 27, 2. 

Micrograph, 6, 8. 

Mildness, coeflicient of, 11, 19. 

Military explosives, 2, 9. 

Mill cake, 4, 8; gunpowder, 4, 1; 

train, 15, 43; universal, 

15, 43. 

Milling, 17, 13,28,28. 

Mi lis metal, 15, 20. 

Mixing gunpowder, 4, 7, 16, 44. 

Modulus of elasticity, 15, 4, 19, 22. 

Moistening gunpowder, 4, 7 ; 
molds, 17, 2 

Molding, 17, 1, 10; composition, 

17, 2; tools, 17, 6. 

Molded gunpowder, 4, 10 ; 

press for, 4, 15. 

Moncriefl carriage, 22, 13, 

Morse cartridge, 27, 5, 28, 22. 

Mortar, 1, 1, 21, 17, 19,22; car- 

riage, 23, 7; fire, formula; for, 

20, 6, 8; fuze, 18, 9; wagon, 

22, 28. 

Mounts, for rapid fire guns, 29, 18. 

Mountings, email arm, 28, 5, 

Mu ifi), 11, 19 

Mule, 24, 1. 

Muzzle loading projectiles, 5, 3, 16, 12. 



N. 

Napoleon gun, 21, 4. 

Nasmyth hammer, 15, 45. 

Natural line of sight, 30, 2. 

Nave, 22, 22. 

Nickel armor, 16, 43; in steel, 

15, 20. 
Nitrates, 3, 6, 12,29. 
Nitre, 3, 6. 
Nitro-benzine, 14, 15; glycerine, 

14, 11. 
Niven's method, 20, 25. 
Noble's gauge, 7, 4; experiments, 

7, 16, 9, 1; — an(i Abel's law, 
9,8, 



INDEX. 



Nolan range finder, 30, 20, 
Non-metallic cartridges, fil, 2. 
Non-recoil guns, as, 18, 29, 1 ; 

mount, 29, 19. 
Nordenfelt gunpowder, 4, 15; 

machine gun, 89, S; rapid fire 

gun, 29, 24. 
Nucleus, 30, 6. 
Number of grains varied, 10, 2. 



Oblong projectiles, advantages of, 16, 

4. 
Obturating primers, 18, 4. 
Oil hardening, 15, 53, 57. 
Open hearth process, 15, 37; 

steel, 16,14,32. 
Orders of explosion, 3, 2, 4. 
Ordnance, I, 1. 
Origin of motion, .1,10. 
Oxidation, rate of, 15, 37; scale 

of, 16, 17. 
Oxydizing agents, 3, 6. 



P. 

Pack horse, 84, 1. 

Palliser gun, ai, 5. ' 

Parallax, 30, 11. 

Parrott gun, 21, 5 ; i)rojectile, 

16. 12. 

Parting plane, 17, 4; sand, 17, 3. 

Passive resistances, 11, 8. 

Patterns, 17, 3, 7. 

Pebble powder, 4. 12, 13, 5. 

Peep sight, 30, 4. 

Percussion caps, 18, 2; fuze, 18, 

11. 
Pemot furnace, 15, 30, 41. 
Petroleum fuel, 15, 38. 
Phi dash(g)), 20, 22, 37, 50. 
Phosphorus in steel, 15, 19. 
Physical constants, 24, 2, 28, 17; 

properties, 15, 1, 12, 20, 57. 
Pi (FT), coj^fficient, 11, 27, 12, 29. 
Picric acid, 1 4, 17. 
Piemonte S. S., 29, 17, 
Fiutles, ^^, 9, 36.. 



Piping, 15, 21. 

Plane table, 30, 14. 

Platforms, '4a, 19. 

Pointing, 20, 1, 30, 1. 

Porter bar, 16, 56. 

Ports, 22, 14. 

Potasaum chlorate, 3, 7, 14, 16, 19. 

Potential, », 6, 9, 7; work, 2, 6, 

II, 9, 15, . 

Pouring, 17, 7. 

Powder mills, 4, 1. 

Pratt range finder, 30, 17. 

Precautions in manufacture of gun- 
powder, 3, 5, 4, 1. 

Premature explosions, 18, 19, 21, 14, 
28,6. 

Preponderance, 1, 2, 22, 8. 

Press cake, 4, 7; forging, 16, 47; 

powder, 4, 9, 15. 

Pressure curve, 9, 13, 11, 3, 12, 8, 
19, 46. 

Pressure, exterior limits of, 19, 39; 

formula;, Sarrau, 12, 8, 13; 

gauges, 7, 1, 5; in gun. Noble 

and Abel, 9, 11; ■ high explo- 
sives, a, 8, 14, 4; piston, mass 

of, r, 6. 

Primers, 14, 3, 18, 1, 3. 

Probability of fire, 30, 27. 

Probable error, 30, 32; rectangle, 

30, 34; zones, 30, 33. 

Products of gunpowder, 2, 10, 11, 29; 

of high explosives, 2, 2, 14, 

4. 9, 12. 

Profiling, 28, 28. 

Profile of i)rojectile, 16, 16, 20, 9. 

Progressiveness, 10, 3, 11, 19. 

Progressive range finding, 30, 21. 

Projection, angle of, 20, 2. 

Projectiles defined, 16, 1; form 

of, 5, 3; manufacture of, 1 7, 1; 

proof of, 17, 16, 18. 

Proposed magazine arm, 2S, 13. 

Proportions of cannon, 5, 2, 9, 13, 13, 
2, 19, 6, 46. 

Puddled steel, 15, 30. 

Pulls, 15, 44. 

Pulverizing gunpowder, 4, 6, 

Funching armor, 16, 36, 



iJ^i)E5t. 



Quadrant an^le, 20, 2. 

Quenching 15, 22, 49. 

Quickness of gunpowder, 11, 7,24, 12, 

10, 12, 29. 
Quick loader, 38, 13. 
Quick match, 1 8, 1. 



Rackarock, 14, 15. 

Racking armor, 16, 36. 

Radius of gun, 20, 1. 

Ramsbottam's hammer, 15,47. 

Range, 20, 4 ; to compute, 20, 36; 

finding, 30, 10; table, 30, 

8, 52. 

Rapidity of lire, 27, 2; 28, 1; 29, 1, 7, 
11, 16, 17, 26, 30, 61; of re- 
action, 2, 8. 

Rapid firing guns, 21, 1, 29, l, 16. 

Reaction, gunpowder, 2, 10; gun 

cotton, 14, 9; nitro-glycerine, 

14, 12; rapidity of, 2, 8. 

Re- annealing, 15, 67. 

Recoil, angle of greatest, 22, 9; of 

cannon, 11, 18, 19, 19; control 

of, 22, 11; — energy of, 19, 19, 2'^, 

3; extent of, 22, 7, 11, 16; 

force of, 22, 5; mount, 29, 19; 

periods of, 22, 3; pheno- 
mena of, 22, 8; rotation due 

to, 22, 8; small arms, 28, 16; 

in testing metals, 15, 3; 

work of, 15, 5, 22, 4. 

Refining steel, 15, 52. 

Regenerator, 15, 39. . 

Reheating furnace, 15, 45. 

Remeltlng iron, 15, 24, 

Reinforce, 1,2. 

Resistance of air, 20, 8, 16; of 

cannon, 19, fi, 31, 3:5; passive, 

11, 8; of primers, 18, 4. 

Retardation, coefficient of, 16, 2. 

Reverberatory furnace, 15, 25. 

Revolvers, 28, 23. 

Ricqs register, 7, 15. 

Rifle, 28, 1. 

Rifling, 1, 2, 16, 8, 28, 3, 27. 



Right line method, 30, 41, 45. 

Rigidity of trajectory, 20, 24. 

Rimfire cartridge, 27, 3. 

Rimless cartridge, 28, 23. 

Riser, 17, 9. 

Rockets, 16, 44. 

Rodman's gauge, 7,3; gun, 19,12; 

improvements in gunpowder, 

13, 3; velocimeter, 6, 13, 7, 12. 

Rolls, 4, 3, 

Rolling mill, 15, 43; — ^ table, 17, 17. 

Rotating bands, 17, 15; device, 

11, 16, 16, 12, 15. 
R^ation of projectile, 11, 16, 16, 12. 
Rotary energy, 16, 3; furnace, 

15, 37, 41. 
Rotten steel, 15, 18. 
Rumford's gauge, 7, 2. 
Rupture of shells, 16, 19. 
Russell's interrupter, 6, 13. 



Saber, 26, 2. 

Safe space, 20, 39, 43, 30, 51. 

Saltpeter, 3, 6. 

Sand, molding, 17, 3. 

Sarrau, application, 12, 21, 28 ; 

formulae, 12, 1; on pressure 

gauge, 7, 8. 

Sawyer canister; 16, 25. 

Schulhofl" magazine rifle, 28, 13. 

Screw guns, 21, 17; interrupted, 

21, 10. 

Sea coast cannon, 21, 20; car- 
riage, 23, 5; fuze, 18. 9. 

S6bert's projectile, 7, 10; veloci- 
meter, 6. 13, 7, 13. 

Sectional density, 16, 1, 28, 21. 

Segment shell, 16, 33. 

Segregation, 15. 16, 59. 

Sensitiveness of high explo.sives, 14, 2. 

Set of metal, 15, 3; of wheel, 22, 

24. 

Shafts, 22, 28. 

Sheaf of dispersion, 16, 23, 30, 6. 

Shearing plane, 27, 4. 

Shear steel, 15, 30 

Shells, 16, 18; bursting charges, 

14, 7, 19, 16, 20, 33, 19, 17. 



10 



1NDE5^. 



Shields for guns, 16, 41, 23, 6. 

Shock, explosion by, 8, 2, 14, 3, 7, 12, 
15, 16, 16, 21, 18, 11. 

Shortening bore, 7, y. 

Shrapnel, 16, 23, 26; early, 16, 30; 

fire, 16, 34. 

Shrinkage in cannon, 15, 21, 58, 19, 
12, 15, 23, 41. 

Shuts. 15, 44. 

Side-box, maxim, 29, 27. 

Siege cannon, 21, 17; carriage, 

«3, 3. 

Siemen's furnace, 15, C9; regene- 
rator, 16, 3!). 

Sights, 20, 1, 28, 4, 20, 30, 1; 

angle of, 20, 2; field, 30, 3; 

heavy guns, 30, 3; line of, 

20, 1; plane of, 20, 4; 

radius, 20, 1; small arm, 28, 4. 

Signal time, 6, 1, 12. 

Silico-Spiegel, 15, 18, 28. 

Silicon as fuel, 15, 35; in steel, 

15,18. 

Similitude, principle of, 1^, 14. 

Sinclair check, 22, 12. 

Singletree, 22, 27, 24, 5. 

Sinking head, 15, 34, 58, 17, 10, 15. 

Single cylinder, strength of, 19, 6, 31. 

Size of grain, 10, 2, 11, 4. 

Slide rest, 17, 11. 

Sling cart, 25, 2. 

Slow match, 18, 1. 

Small arms, 1, 1, 28, 1; ammuni- 
tion, 27, 1, 9; manufacture of, 

28, 24. 

Small caliber, 28, 2, 20. 

Smokeless gunpowder, 3, 7, 14, 15, 
28, 22. 

Soaking pits, 15, 43. 

Sodium nitrate, 3, 6. 

Solid head cartridge, 27, 5. 

Solid shot, 16. 18. 

Special irons, 15, 27. 

Specific gravity of gunpowder, 9, 3; 
of iron, 16, 24. 

Specific volume, 2, 7, 9, 3, 7. 

Spheres of action, 14, 5. 

Spherical case. 16, 31; density, 12, 

31, 16,6, 28,21. 



Spiegeleisen, 15, 28. 

Spindles, lathe, 17, 11. 

Sprengel mixtures, 14, 16. 

Springfield rifle, 28, 15. 

Stationary carriages, 2'4, 1. 

Stadia, 30, 13. 

Static measures, 7, 2 

Steam, comparison to, 11,1; test, 

17,17. 

Steel castings, 15, 42; cast can- 
non, 15, 58; classification of, 

15, 13, 18; composition of, 15, 

17; constitution of, 15, 16; 

manufacture of, 15, 30; me- 
chanical treatment of, 15, 4 ; 

molecular treatment of, 15,48; 

projectiles, 16, 6; projectiles, 

manufacture, 17, 14; proper- 
ties under stress, 15, 22; struc- 
ture of, 16, 20, 49; working 

properties, 15, 22. 

Stock, cannon, 22, 3, 25; rifle, 28, 3. 

Stone projectile, 16, 5. 

Store wagon, 22, 29. 

Strain diagram, 15,3,8; equalizing, 

19, 9, 19, 23; internal, 15, 21, 

55, 19, 12; as function of 

radius, 19, 3, 29; on gun, 5, 2, 

16,3, 19,1. 

Strength of cannon, 5, 1, 2, 1 9, 6, 31, 33; 

of explosives, 2, 6; of gun 

construction, coeflicient for, II, 
21. 

Stress and strain, 16, 1, 19, 22; in 

guns, 5, 2, 16, 3, 19, 1. 

String measure, 30, 24. 

Structure of projectiles, 16, 17. 

Studded projectile, 16, 12. 

Successive means, method of, 30, 21; 
shortening of bore, 7, 11. 

Sulphur, 3, 1; in steel, 15, 20. 

Supply train, '-i'-i, 29. 

Surface of gunpowder, 8, 1, 10, 1. 

Sweep molding, 17, 3, 5 

Swiss method, 30, 27. 

Sword, 26, 1. 

Sympathetic detonation, 2, 5. 

System of artillery, 21, 3; at rest, 

etc, 19, 13, 36. 



INDEX. 



11 



Tarage, 7, 7. 

Targets, animate, 30, 48; —— comput- 
ing, 30, 26; velocity, 6, 14. 

Team, arrangement of horses, 24, 5. 

Telescopic sight, 30, 3. 

Telemeters, 30, 11, 

Temperature of ignition, 8, 1, 14, 3; 

of explosion, 2, 8, 9, 8; 

scale of, 1, 3. 

Tempering, 15, 52. 

Tenacity, 15, 10. 

Testing cannon metal, J 5, 57; 

machines, 16, 1,5; projectiles, 

17, 18. 

Test piece, form of, 16, 2; record, 

15, 2, 8. 
Thickness of cannon, 5, 2, 9, 13, 19,6, 

19, 45, 46. 
Thrusting arms, 86, 1. 
Thurston machine, 15, 6. 
Tilted steel, 15, 30. 
Time of flight, 30, 40, 41, fuze, 16, 

18, 18, 6, 10; limits, 6, 8; 

of maximum, 13, 11. 

Tire rolling, 15, 44. 

Tolerance, 4, 11, 17, 17. 

Tonite, 14, 9. 

Torpedo shells, 14, 8, 16, 20, 31, 18. 

Torsional testing, 16, 6. 

Trajectory in air, 30, 18; curva- 
ture of, 1, 3, 30, 23; elements 

of, 30, 30; flatness of, 1, 3. 30, 

23, 40, 38, 20, 30, 35, 30; mean 

radius of curvature, 30, 23; 

rigidity of, 30, 24; in vacuo. 

30,6. 

Traveling trunnion bed, 33. (. 

"Treatment" of cannon, 15, 57. 

True mean error, 30, 33, 41. 

Trunnions, inclination of, 30, 2. 

Tubular magazines, 38, 10. 

Tuning fork, 6, 12, 7, 13. 

Tumbling barrels, 4, 4; of pro- 
jectiles, 16, 3. 

Turning angle, 33, 25. 

Twist, 10, 9, 



U. 

U, path of projectile, 11, 10, 14, 13, 1. 
Units of measure, 1, 3. 

V. 

Vacuo, trajectory in, 30, 6. 

Value of explosives, 3, 8, 14, 2. 

Variables, experimental, 9, 1. 

Varying elasticity, 19, 9. 

Velocimeters, 6, i, 7, 9; Benton, 

6, 3; classified, 6, 2. 

Velocities defined, 1, 2; final, 30, 

17; formula;, 13, 5, 12; 

targets, 6, 14. 

Vents 11, 18, 31, 13; direction of, 

18, 3; rocket, 16, 44. 

Vertex, height of, 30, 36; prin- 
ciple of, 30, 42. 

Very's formula for armor, 16, 41. 

Vesiculation, 15, 21. 

Volumes of expansion, 11, 12. 

Vulnerability, 30, 50. 

W. 

Wagon, mortar, 33. 28; store, J5J5, 

29. 
Washed metal, 15, 19. 
Waste of energy, 9, 10, 11, 8. 
Water on high explosives, 14, 5, 6; 

annealing, 15, 54; cap, 

18,9. 
Weather, 30, 9, 30, 10. 
Weaver formula for armor, 16, 42. 
Weight of cannon, 6, 1, 19, 19; of 

charge, Jl, 13, 15, 13, 16, 32, 38, 

21; distribution of, «3, 4, 34, 

2, 38, 17; of projectile, 16, 8. 

Weld steel, 15, 14. 
Weldability of metals, 15, 23. 
Weldon range finder, 30, 16. 
Wertheim's coefficient, 19, 2, 3, 25. 
West Point target, 6, 15. 
Whitvvorth's forging press, 16, 47; 

projectile, 16, 12, 17; 

steel, 16, 15, 34. 
Wheel mills, 4, 7; principles <jf, 

33, 21. 



12 



INDEX. 



Wheeled carriages, 23, 2. 
Wiener's powder, 4, iO. 
Wiliiston harness, 24, 8. 
Winchedter magazine rifle, 28, 10. 
Windage, 1, 2. 
Wind and accuracy, 30, 9. 
Wire drawing, 15, 44; wound can- 
non, 19, 17. 
Woodbridge gun, 19, 18. 
Woods, physical properties of, 16, 11 . 



Work of gunpowder, 3, 6, 9, 7, 11, 10. 
Wrapped metal cartridge, 87, 7. 
Wrought iron, manufacture, 16, 29; 
projectiles, 16, 5. 



Zalinski gun, 10, 3, 14, 8. 
Zones in collective fire, 30, 49. 
Zones, probable, 30, 33. 



I. — DEFINITIONS. 



- 07 THr: 



^TJKITEBSIT 



CHAPTER I, 



DEFINITIONS. 

Ordnance. — A general terra usually applied only to the 
material of Artillery, but embracing also all warlike stores 
made according to prescribed regulations or ordinances. 

Fire Arms. — Offensive weapons used to throw projectiles 
by means of explosives. They are divided into — 

1. Cannon. — Heavy fire arms requiring carriages to sup- 
port and to transport them. 

2. Small Arms, — Which can be carried by men. 
Cannon are divided into — 

Guns. — Or relatively long cannon. Gun is used as a gen- 
eral term for all fire arms. It has probably the same root 
as engine, meaning a machine. 

Howitzers.. — Comparatively short cannon. 

Mortars. — Very short cannon. 

NOMENCLATURE. 

Bore. — That part of a cannon which is bored out. It in- 
cludes — 

1. The cylinder or principal portion of the bore.' 

2. The seat of the charge, or the part occupied by the 
powder. This may be either a continuation of the cylinder 
terminated by a plane or curved surface; or a cha?nder, the 
diameter of which differs from tha* of the cylinder of the 
bore. For breech loaders, the chamber is divided into the 
powder chamber and the shot chamber. 

Caliber. — The diameter of the cylinder of the bore. It was 
formerly expressed by the weight of the inscribed sphere. 



I. — DEFINITIONS. 



For cannon, this was the weight in pounds of the cast iron 
shot; for small arms, the number of leaden balls required to 
weigh a pound. 

Rifling. — Cutting spiral grooves in the surface of the bore, 
so as to give to the projectile a motion of rotation at right 
angles to that of translation. 

Lands. — The ridges left between the rifle groves. The 
caliber of rifles is usually measured between lands. 

Chase. — The long conical portion of a cannon in rear of 
the muzzle. 

Reinforce. — The thick portion of the body over and imme- 
diately m front of the seat of the charge. 

Breech. — The mass of metal in rear of the plane of right 
section at the base of the charge. 

Line of Metal. — The intersection of the upper surface of 
the piece by an axial plane perpendicular to the axis of the 
trunnions. 

Dispart. — The difference between the semi-diameters at 
the muzzle and at the breech. 

Preponderance. — The difference between the moments of 
the weight in front of, and in rear of, the trunnions. 

Windage. — This is properly the difference between the 
area of right section of the cylinder of the bore, including 
the grooves, and the maximum parallel area of right section 
of the projectile. 

It is usually expressed in linear units as the difference 
between the diameter of the cylinder of the bore and the 
diameter of the projectile. 

VELOCITIES. 

Muzzle or Initial Velocity. — Is the maximum velocity of 
the projectile after leaving the piece, 



t. — BEFmiTlONS. 



Remaining Velocity. — Is that at any point of the trajec- 
tory. 

Terminal Velocity. — Is that at the point of impact. 

The greater the velocity at any instant, the more flat does 
the trajectory become; and, therefore, the greater is the 
probability of striking a vertical object at an unknown 
distance. (See note 1, page 5.) 

The horizontal distance over which, under given condi- 
tions, a vertical object would be struck, is called the dan- 
gerous space for that object. 

UNITS OF MEASURE. 

Those used in English speaking countries are unfortun- 
ately numerous and are apt to cause confusion. 

Units of Temperature. 

Throughout this work the temperatures are expressed in 
degrees centigrade. 

Units of Length, 

Yards. — For ranges of projectiles. 

Feet. — For measuring velocities and the chords and alti- 
tudes of trajectories. 

Inches. — For the internal dimensions of guns and for all 
dimensions of their projectiles. The decimal sub-division 
of the inch is generally employed. 

Units of Weight, 

Tons. — For cannon, 1 ton =2240 lbs. 

Pounds. — For large projectiles, for their charges and for 
measuring the pressures (per square inch) of the gases of 
fired gunpowder. 

In England, pressures are measured in tons per square 
inch; in France, in kilogrammes per square centimetre; else- 
where on the continent of Europe in atmospheres. 



t. — MFiNitioNS. 



Grains Troy. — For bullets and powder charges of small 
arms 7000 grains troy=l lb. avoirdupois. 

g is generally taken =32.2 lbs., which is nearly its value at 
London. 

Unit of Energy and Work, 
Foot tons=foot pounds-r2240. 

USEFUL MECHANICAL FORMULAE. 

s 



Uniform motion, v=- 

ds 
Varied motion, v— —r: 



Uniformly varied motion, v=-aJ<^ a-k = a-fj h— — 

% 

. . dv d^s 

Acceleration, af= -T- = -To- . 
at dt^ 

Intensity of a motive force, I=Ma. 

Intensity of an impulsive force, I^-^MV, 

Measure of work, Q=Wh—flds, 

Measure of energy, E= ^f^^ 

Time of oscillation of a simple pendulum, t=;rA / — 

ABBREVIATIONS. 

S. B. — Smooth bore. 

R.— Rifle. 

M. L. — Muzzle loading. 

B. L. — Breech loading. 

C. I. — Cast iron. 

W. I. — Wrought Iron. 
S._Steel. 

The caliber is placed first. Example: 
8 in. B. L. R. S. 



1.— i>EpmiTtoNS. 



15 in. S. B. C. I., etc. 

W. w. — Weight of larger and smaller of two masses consid- 
ered; as of piece in regard to projectile, or of projectile in 
regard to charge of powder. 

V. V. — Initial and remaining velocities. 

p. — Intensity of gaseous pressure per unit of area. 

r. d. — Radius and diameter of the cylinder of the bore, or 
of the projectile according to context. 



Note 1. From Michies Mechanics, Article 94, we have — = '^ ^^ 
See also Chapter XX, p. 22. p "v , 



!I. — EXPLOSIVE AGENTS. 



CHAPTER II. 

EXPLOSIVE AGENTS. 

Explosion. 

Is a name given to a series of phenomena resulting from 
two general causes. 
Causes of Explosion. 

I. The rapid conversion of a solid or liquid to a gaseous 
state. This conversion is accompanied by the evolution of 
heat, due to the nature of the chemical reaction involved. 

II. The rapid dilatation of a mixture of gases by the heat 
evolved in their combination. Such explosives are not yet 
generally employed in warfare and are not herein considered. 
Products. 

The gases evolved in conversion are principally CO2 and 
CO. These result from the more or less perfect combustion 
of carbon, which enters into every military explosive under 
circumstances intended to facilitate its oxidation. 
Dissociation. 

The tendency at high temperatures of CO2 and other com- 
plex products to occur in simpler forms, as CO + O, is sup- 
posed by Berthelot to exert a powerful influence upon the 
corresponding pressures. 

Dissociation, as this phenomenon is called, whether it pre- 
vents the formation of the complex product or destroys it, 
increases the specific volume of the gaseous products; but, 
since Mariotte's law has been proved not to hold for pres- 
sures ^ of those found in fire arms, it is supposed that the 
loss of heat from imperfect combination, or from work done 



II. — EXPLOSIVE AGENTS. 



in breaking up the molecules already formed, exceeds in its 
effect upon the resultant pressure the increase of specific 
volume cited. External causes may subsequently decrease 
the temperature and permit recombination with a relative 
increase of pressure. 

It is found that, when the conversion yields a large pro- 
portion of CO, the violence or sharpness of the explosion is 
increased. This is supposed to be due to the rigidity or 
stability of this gas against diSvSOciation. 

H2 O is, by some, supposed to be subject to dissociation 
at the temperatures found in explosions. (See Bloxam, Arts. 
36, 68, 311, Note.) 
Firing. 

The proximate cause of the reaction resulting in an explo- 
sion is always the absorption by some portion of the explo- 
sive of heat sufficient to raise its temperature to the point 
necessary to start the conversion. 

The source of heat may be external; or, as in spontaneous 
decomposition, internal. 

The means by which the temperature of the explosive is 
raised to the critical point may, in general terms, be called 
firing. 

Firing generally results from the transformation of kinetic 
energy into heat as a result of arresting the motion of either 
molar or molecular masses. 

Almost all explosives may be fired by molar shock, if it be 
concentrated on a mass of the explosive which is sufficiently 
small. (Bloxam, Arts. 309, 434, 538). 
Orders of Explosion. 

The energy of molecules in motion depends principally 
upon their velocity; and the external work done in stopping 
them, upon their stability of composition. When an explo- 
sive is fired by contact with incandescent matter, as by a 
flame consisting of molecules of COg, C, etc., moving with 



II. — EXPLOSIVE AGENTS. 3 

relatively low velocities, the explosive is said to be ignited^ 
and the explosion is called low or of the second order. 

When fired as by fulminate or gun cotton, the conver- 
sion of which yields a large proportion of molecules of CO, 
moving with a very great velocity, the explosive is said to 
be detonated, and the explosion is called high or of \.\\& first 
order. ■ Explosives which readily detonate are called high 
explosives. 

Example, Gun-cotton when — 

Order. 

Ignited j unconfined; burns quietly — 

^ * * ' ( confined; explodes like gunpowder 2nd 

unconfined ) i j vu 

[ explodes with great 



f violence 1st 



Detonated . . . -j or 

( confined; 

The distinction between the two orders of explosion is 
only conventional; the phenomena in practice appearing 
often to partake of the nature of both orders. 

This may explain certain anomalies observed in mining 
and in artillery. In mines, when the charges are large, the 
high pressure resulting from the initial explosion, if at a 
point considerably beneath the surface of the charge, is sup- 
posed to cause the detonation of the remainder. In cannon 
the mixing of quick with slow powder produces a similar 
effect. 



BERTHELOT S THEORY OF EXPLOSIVES. 

Origin of Reactions. 

" Every explosion must be referred to some initial increase 
of temperature transmitted from particle to particle on the 
surface of an explosive wave. This wave raises successively 
all portions of the explosive to the temperature of convei- 
sion. 



II. — EXPLOSIVE AGENTS. 



Propagation of Eeactions. 

Two limiting conditions are supposed to result, viz.: 

1. The condition of combustion. 

2. The condition of detonation. 

These are progressively interchangeable in different de- 
grees, according as the amplitude and velocity of vibration 
of the particles forming the surface of the explosive wave 
are increasing or diminishing. 

Combustion. 

I. The condition of combustion depends upon a reduc- 
tion of temperature from the free expansion of a portion of 
the gases resulting from the initial explosion. 

Successive portions of the explosive will thereupon be 
heated to the temperature of decomposition with a velocity 
depending upon various conditions; this velocity, compared 
with that of detonation, is slow. 

Detonation. 

II. On the other hand, the condition of detonation de- 
pends upon an initial shock, too sudden (sharp) to permit of 
molar motion of the particles of the explosive. It is, there- 
fore, transmuted into heat which may raise the contiguous 
molecules to the temperature of conversion. The result- 
ing gases arc projected as a single (not periodic) explosive 
chemical wave traveling throughout the successive layers of 
the unexploded mass. This wave transforms its energy into 
heat at each impact, and, by virtue of its acceleration, raises 
each of the successive layers more rapidly to the tempera- 
ture of conversion. 

Origin of Orders of Explosion. 

The order of the resulting explosion will depend upon the 
velocity with which the reaction is propagated; /. ^., the velo- 
city of the wave surface described. 

The velocity of the wave surface will depend — 



n. — EXPLOSIVE AGENTS. 



1. Upon the molecular velocit}^ of the reaction; /. ^., the 
rate of conversion under constant conditions. 

2. Upon conditions which prevent the free expansion of 
the gases formed. 

3. Upon the mass and initial temperature of the explo- 
sive; these affect the rate of cooling. 

The last two conditions may be neglected when, as with 
the high explosives, the first is fully satisfied. 
Influence of Detonator. 

It is seen that detonation depends upon a chain of causes 
which results from the nature of the initial explosion. Herein 
lies the importance of the nature of the detonator, its mass, 
and the nature of its own explosion. 

Its conversion should be rapid and evolve abundant heat. 
The mercuric fulminate is the detonator which is preferably 
employed. It is less violent than NCI, but yields more heat 
by its explosion and also much CO. 
Influence of the Explosive detonated. 

Detonation depends upon the physical condition of the 
explosive. Its sensitiveness generally diminishes as its den- 
sity and elasticity increase, since the shock is distributed 
over a greater mass." 

SYMPATHETIC DETONATION. 

Conditions. 

The instability of the high explosives renders their con- 
tact unnecessary when the continuous detonation of several 
charges is desired. The maximum interval permitting ''sym- 
pathetic detonation," or "detonation by influence," and the 
order of this detonation, depend upon the elasticity of the 
intervening medium, the mass of the primitive charge, and 
the order of its explosion. 
Examples. 

Calling w the weight of the primitive charge in pounds, 
and d the maximum interval in feet — 



n. — EXPLOSIVE AGENTS. 



In water, d=S w. 

On a firm soil, (/=5 w. 

On an iron rail, ^=10 w. 

When discs of compressed gun-cotton are in contact, the 
velocity of detonation is said to be over 3J miles per second 
when the discs are wet, and less than 3J miles per second 
when they are dry. The incompressibility of the water assists 
in transferring the shock. 

STRENGTH OF EXPLOSIVES. 

The strength of an explosive, or its mechanical efificiency, 
may be analyzed by reference to 1, its potential; 2, its force; 
3, the molecular velocity of its reaction. 

1. Potential. 

The potential of an explosive is the maximum work 
which a unit weight of it can perform. It is measured by 
the product of the quantity of heat liberated by the reaction, 
and the mechanical equivalent of heat; or, Q= J x H. 

The potential is independent of the process of conversion, 
provided it be complete and its products be constant. 

In practice, these products often vary with the circum- 
stances under which they are formed, so that the potential 
realized will also vary. 

Only a portion of the potential can be realized in prac- 
tice, depending upon the volumes of the gases produced, 
their specific heats, and the difference between the tempera- 
tures at which they are formed and to which they are ex- 
panded. 
Examples.* 

Theoretical potentials, in foot tons, resulting from the 
conversion of one pound of each of the following sub- 
stances: 



* It is required that only the general principles illustrated by this and 
following tables shall be committed to memory. 



II. — EXPLOSIVE AGENTS. 



Name. Foot Tons. Proportion. 

Blasting powder 391 1.0 

Cannon " 609 1.3 

Sporting « 642 1.4 

Gun-cotton 716 1.8 1.0 

Dynamite No. 1 884 2.3 1.3 

Explosive Gelatine 1,235 3.2 1.8 

Nitro-glycerine 1,282 3.3 1.8 

Chloride of Nitrogen 216 0.5 

Anthracite coal 6,170 13.0 

The greater potential of coal is due to its composition and 
to there being no loss of energy expended in converting in- 
to gas the compounds of oxygen contained in the other sub- 
stances. 
2. Force. 

The force of an explosive, or the pressure per unit of area 
due to the explosion of a unit of weight in a unit of volume, 
may be calculated on theoretical grounds from the formula,* 

In which v^ is what is known herein as the specific volume of 
the gas, viz.: the volume in litres of the gases resulting from 
firing one kilogramme of powder, taken at 0° C, and at the 
pressure p^ of one atmosphere ; and c is the specific heat of 
the gas. 

But the uncertainty attending the application of the laws 
of Mariotte and Gay-Lussac to such high pressures as exist 
in cannon, and the doubt as to the nature and state of the 
products of explosion at the epoch of maximum pressure 
have caused instrumental measurements of pressure to be 
preferred. 

Examples. 

The following table shows in round numbers the relative 
force of the explosives named. 



* For the deduction of this formula see page 11. 



II. — EXPLOSIVE AGENTS. 



The detonation of gunpowder was accomplished by mix- 
ing it with dynamite. 

Eelative Force. 
Explosive. 1st Order. Snd Order. 

Gunpowder 4.0 1.0 

Gun-cotton 6.0 3.0 

Nitro-glycerine 10.0 5.0 

The force of a mixture of high explosives is proportional 
to the sum of the products of the force of each constituent 
by the corresponding fractional part of the whole mass. 

A remarkable property of gunpowder (to be referred to 
hereafter) is that, however its potential may vary with its 
composition, the force of all compositions is sensibly con- 
stant. The specific volume of the gases formed seems to 
vary inversely with the quantity of heat evolved in their 
formation. 

3. Rapidity of Reaction. 

The temperature increases with the rapidity of the reac- 
tion. This depends upon the affinity between the combin- 
ing molecules, and largely upon the state of aggregation 
of the exploding mass, in so far as it affects the distances 
between them. 

In certain high explosives, the rapidity of the reaction 
causes so high a temperature that the gaseous products are, 
as it were, shot against the w^alls of the envelope with such 
velocity that the effect seems due rather to a physical shock, 
than to the elastic pressure of a confined gas. With such 
explosives tamping is relatively unneccessary. 

VALUE OF EXPLOSIVES. 

As a general rule, the value of an explosive depends: — 
1. Mechanically; upon its primitive state of aggregation, in 

so far as this affects the ease of handling it in loading; also 

upon its density. 



II. — EXPLOSIVE AGENTS. 



V H 
2. Chemically; upon the value of the ratio —2 — z=iv^T^ 

If, when this is great, the conversion is sufficiently rapid, a 
high and elastic pressure will succeed the initial shock; this 
pressure will be well sustained, since the cooHng effect of 
the envelope will be relatively small. 

The potential of an explosive is thus seen to be the 
measure of its power of sustaining a given force or pres- 
sure. 
Examples. 

The relative importance of potential, force, and rapidity, 
depends upon the use made of the explosive. 

In order to burst, we use one of high force and density, 
acting locally like an hydrostatic pressure. 

Chloride of nitrogen detonates with such rapidity that it 
may simply pulverize the surface of the envelope without 
rupturing its walls. 

For mining in rock or coal, blasting powder is better than 
cannon powder, since the end sought is rather the rup- 
ture of the envelope than the dispersion of the fragments. 
Its force depends on the great specific volume of the gases 
generated rather than upon their temperature. 

For blasting in earth, cannon powder is better than blast- 
ing powder as its potential is higher. Its diminished den- 
sity, compared to high explosives, distributes the effect over 
a larger area. 

MILITARY EXPLOSIVES. 

The principal explosives used in warfare are of two 
general classes: 

1. Mixtures. 

Gunpowder and its like; these are more or less inti- 
mate mechanical mixtures of combustibles, such as C, S, Sb, 
with an oxydizing agent, generally a nitrate or a chlorate. 



10 ■ II. — EXPLOSIVE AGENTS. 

Explosives of class 1 are relatively stable. 

2. Compounds. 

Nitro-glycerine and gun-cotton and their derivatives. 
These are chemical compounds, formed by the substitution, in 
an organic substance of the general form C^ Hy 0„ of 
3 molecules of NO2 for 3 atoms of H. 

The weak affinity of N renders the NO^ a readily acces- 
sible magazine of oxygen. 

Explosives of class 2 are called high explosives, and 
are relatively unstable. In this class are included the 
fulminatmg compounds. See Chap. XIV. 

GUNPOWDER. 

This is formed of a mixture of KNO3; C, and S, in the 
proportions of about 75, 15, 10. These proportions are 
considerably varied in pyrotechnic compositions. 

The conversion of gunpowder is approximately expressed 
by the following reaction: 

4KN03-|-Q + S=K2C03 + K2S04 + N,-i-2COa4-CO. 

The reaction is really much more complex, and varies 
with the circumstances attending the explosion, even 
though great care be taken to make them constant. 

Illustration. 

The parts played by the three ingredients may be im- 
agined by reference to the forced combustion of coal in a 
furnace. 

The charcoal, in which form C is introduced, forms the 
main supply of fuel. The sulphur, owing to the ease with 
which it is ignited, takes the place of the kindling material. 
The nitre acts as a bellows forcing in air. 

The sulphur also gives coherence to the grain, correct- 
ing the friability of a binary mixture of carbon and nitre. 



11. — EXPLOSIVE AGENTS. 11 

Advantages and Disadvantages. 

The facility with which, by varying the proportions and 
the arrangement of the ingredients of gunpowder its 
conversion may be controlled, and also its comparative 
stability against accidental ignition, have hitherto com- 
pensated for its defects. 

These refer to its bulk, the care required in storage, its 
sensitiveness to dampness, the large solid residue left from 
its conversion, and the danger attending its manufacture. 
While for special purposes, where great force is required, it 
is being supplanted by the high explosives; its value, as a 
reservoir of potential energy for purposes of propulsion, 
increases as our knowledge of its properties extends. 

Note to page 7. 

1. From the chemistry we have p v =/o ^^o ( 1 H 7 = — 7 ) . If in 

\ 273 ^Tdl 

this we make v = l, then by definition /= p = — — ^ — - = — . 

•^ ^ 273 273 C 



III. — INGREDIENTS OF GUNPOWDER. 



CHAPTER III. 
INGREDIENTS OF GUNPOWDER. 

COMBUSTIBLES. 

1. Sulphur* 
Preparation. 

This is refined by distillation. The product is called 
"flowers of sulphur," or "rock sulphur " or "brimstone," 
according to the temperature at which the volatile pro- 
ducts are condensed. 
Properties. 

If below 115°, minute crystals or "flowers" are formed; 
above that temperature, the vapors condense in a liquid 
form, which is cast into moulds. Flowers of sulphur are 
not used for gunpowder, as they contain SOg and HgSOji 
which are hygroscopic. 

2. Charcoal, 
Material. 

Charcoal used for gunpowder is made from wood, the 
composition of which, excluding water and ash, is repre- 
sented by CeHioOg, corresponding to the following propor- 
tions per cent.: 



c, 


44 


H, 


6 


0. 


50 



100 

The object of carbonizing the wood is twofold. 1st. To 
increase the calorific value of the fuel by increasing the 



III. — INGREDIENTS OF GUNPOWDER. 



proportion of carbon. 2d. To increase its calorific inten- 
sity by facilitating its reduction to powder. 
Composition. 

Gunpowder charcoal consists of from 55 to 85 per cent, 
of carbon with varying proportions of hydrogen, oxygen, 
and ash. Its imperfect distillation leaves varying amounts of 
hydro-carbons which increase its inflammabiUty, and, owing to 
the calorific value of hydrogen, may increase its potential. 
Condition. 

The uniform action of fired gunpowder and the safety of 
its manufacture depend largely upon uniformity in the 
condition of the principal fuel which it contains. 

Uniformity is sought by using the same kind of wood, 
carbonized by the same process; the temperature being 
raised at the same rate to a point which, for each grade of 
charcoal, is the same. 

PREPARATION. 

Preliminaries. 

White woods, such as the young willow or alder, which 
are soft and of rapid growth, are preferably employed, 
since they yield a charcoal that is inflammable, friable, and 
free from ash. 

The bark is removed, so as to facilitate drying in the 
open air, and to free the coal from earthy matter and 
salts. 
Distillation. 

The wood is usually distilled in iron retorts, surrounded 
by flame consisting largely of the gases evolved by the 
process: Figures 1 and 2. 

For convenience, the wood is charged in slips^ which are 
cylinders of thin sheet iron. 

The progress of the operation is judged of by test sticks, 
withdrawn from time to time for examination; by the use of 



HI. — INGREDIENTS OF GUNPOWDER. 



a pyrometer, or by the appearance of the flame and smoke 
as follows. 

Phenomena of Carbonization. 

The rate of distillation being always slow, the character- 
istics of the product depend principally upon the temper- 
ature at which the process ceases. Five stages are recog- 
nized, of which three correspond to useful grades of 
charcoal. 

I. Up to 150°, desiccation occurs. 

II. At 150°, decomposition begins, and continues as fol- 
lows: — 

1st. H and O are evolved and unite. 

2nd. Three acid oxides (carbonic, acetic, and 
pyroligneous acids. — COg; CH3, CO2H; CgH^Og) 
and an empyreumatic oil of an analogous com- 
position are evolved. 

3rd. Soot comes forth in heavy clouds. 

4th. The gases burn with a ruddy flame. 

6th. As the proportion of O diminishes, CO re- 
places CO2, and at 260°, the flame becomes blue. 

The solid products are called brands (Fr. fumer- 
ons)j which smoke in burning. 

III. From 260° to 270°, brown charcoal is formed. It is 
smokeless but tough. 

IV. From 270° to 340° is the period of the formation of 
hydro-carbons; both gaseous, viz.: defiant and marsh gases 
(Cg H^; C HJ, and in various liquid forms, including coal 
tar. The gases burn with a yellow flame, which, as the 
proportion of C diminishes, gradually becomes pale. 

At 280° the liberation of the hydro-carbons changes the 
charcoal from brown to red (charbon roux); it tends to 
raise the temperature suddenly to about 340°. 



III. — INGREDIENTS OF GUNPOWDER. 



The effect of this rise in temperature is to convert the 
red coal to the next grade, which is black. The redness 
of the product will, therefore, depend upon the care taken 
in regulating the temperature. This is done by drawing 
the fire, and completing the process by the residual heat. 

The operation is difficult and the product not uniform. 

V. Above 340°, black charcoal is formed in proportions 
increasing with the temperature, as indicated by the in- 
creasing whiteness of the flame. 

The effect of increasing the temperature upon the pro- 
portions of the constituent elements is shown roughly by 
the following table: 

Max. Temperature.. 150° 260° 280° 350° 

Prr»rln/^fo Dried Brown Red Black 

jrruUUCLb. , Wood, Coal. Coal. Coal. 

Carbon 44.0 68.0 71.0 77.0 

Hydrogen 6.0 5.0 4.5 4.0 

Oxygen 50.0 27.0 24.5 19.0 

Proportion of Weight 

of Dried Wood... 100.0 60 37 30 

Physical Properties. 

The physical properties also change. The higher the 
temperature — 

the more — the less — 

1. brittle; 1. hygroscopic; 

2. hard and dense ; 2. violent as an ingredient 

3. prone to spontaneous com- of gunpowder — 

bustion — 
does charcoal become. 

SPONTANEOUS IGNITION OF CHARCOAL, 

Cause. 

The property of charcoal by which it condenses gases 
within its pores, particularly the vapor of water, may raise 
its temperature to the point of ignition. This ^ facilitated 



in. — INGREDIENTS OF GUNPOWDER. 



by the occluded oxygen and by the increased surface result- 
ing from pulverization. 
Preservation. 

To prevent accident, it is cooled slowly, and kept in the 
stick for several days. To obtain uniformity in the amount 
of water occluded, it is prepared only as required for use. 

Its power of spontaneous ignition, when pulverized, is 
destroyed by mixing it with sulphur or nitre. 

MANUFACTURE OF BROWN CHARCOAL BY SUPERHEATED 
STEAM. 

Process. 

The uniform production of brown charcoal may be 
accomplished by exposing it for a longer period to a some- 
what lower temperature than that above assigned as the 
maximum. For this purpose superheated steam is used, as 
shown in figure 3. 
Eetort. 

The retort is a fixed vertical cylinder of boiler iron, 
jacketed with mineral cotton. (Bloxam, Art. 217.) 

Through perforations in the cast-iron top enters a cur- 
rent of steam which has been superheated in a coil to about 
230°. 

The wood is piled vertically on a perforated false bottom 
made fast to an axial bar, by which the contents can be 
removed. 

The condensed steam and the water, acids, and tar drain 
through the pipe shown. 
Product. 

The process lasts about four hours, being stopped when 
experience shows that the fibrous structure of the wood is 
about to disappear. 

The fiber, which is retained for its binding effect on the 
structure of the powder made from this coal, notably 
increases the difficulty of pulverizing it. 



III. — INGREDIENTS OF GUNPOWDER. 



OXYDIZING AGENTS. 

1. Nitre. 
Source. 

Only about one-tenth of the supply of nitre is the native 
Indian product; the remainder comes from the double 
decomposition of the sodium nitrate with a potassium salt. 

Impurities. 

The principal impurities are the chlorides, the affinity of 
which for moisture renders them objectionable. Not over 
■g-g^ is allowed in nitre used for government gunpowder. 

2. Sodium Nitrate, 
Advantages. 

1. It is cheaper than nitre for equal weights. 

2. Owing to the relative atomic weights of sodium (23), 
and potassium (39), 85 per cent, of the. usual proportion of 
nitre suffices as a supply of oxygen, still further reducing 
its cost. 

3. If the usual proportion of 75 per cent, be retained, the 
greater volume of gas evolved increases the force of the 
powder and adapts it especially for blasting. 

Disadvantages. 

1. The deliquescent properties attributed to the salt are 
detrimental when the powder made from it is to be stored. 

2. The salt is more soluble than nitre, and, therefore, 
powder made from it suffers more than ordinary powder 
from the segregation of the salt by efflorescence. This is 
due to the acqueous vapor condensed in the pores of the 
charcoal which the powder contains. When the powder is 
made on the spot where it is used, as in the excavation of the 
Suez Canal, this objection need not apply. 



III. INGREDIENTS OF GUNPOWDER. 



3. Potassium Chlorate. 
Disadvantages. 

1. The low temperature of conversion, due to the affinity 
of chlorine for the metals, renders the powder dangerous 
when exposed to shock. 

2. Its conversion gives free chlorine, which attacks the 
bore of the gun and is injurious to the gunners. 

3. It is costly. 

4. The uncontrollable violence of mixtures containing 
the chlorates relegates them to the category of the high 
explosives discussed in Chap. XIV. 

They are principally iemployed for igniting other explo* 
5ives; themselves being ignited by friction. 

4. Ammonium Nitrate, 

This is becoming extensively used in the so-called smoke- 
less powders for heavy cannon. 

Advantages. 

The products of combustion are gaseous or volatile, so 
that the smoke is greatly diminished in density, and the 
entire volume occupied by the powder is available for the 
expansion of the gases. 

Disadvantages. 

The deliquescence of this salt requires that powder made 
from it be hermetically sealed. This prevents the use of 
the ordinary cartridge bags. 



IV. THE MANUFACTURE OF GUNPOWDER. 



CHAPTER IV. 

THE MANUFACTURE OF GUNPOWDER. 



ACCIDENTS. 

Buildings. 

Owing to the danger of explosion the buildings are scat- 
tered as much as possible and are separated by traverses or 
rows of trees. Figs. 1, 2. 

The buildings are generally constructed with heavy walls 
on three sides, the remaining side and the roof being as 
light as practicable, so as not to increase the violence of 
explosions by unnecessary confinement. Fig. 3. 

Power. 

The machines employed are usually automatic, power being 
conveyed by canals (fig. 1), or wire rope (fig. 2), radiating 
from a central steam engine. As a general rule safety is 
enhanced by slowly operating the machines. 

Precautions. 

The machines are started and stopped from an outside 
shelter, the completion of the operation being indicated by 
an automatic signal. Great care is taken to prevent the in- 
troduction of foreign matter, the workmen being required 
to change their clothing before entering, and wearing rubber 
overshoes within the buildings, at the door of each of which 
is a wet mat. 

All parts of the machines liable to become loose are boxed 
in. Iron is replaced, wherever possible, by gun-metal, copper, 
or wood. 



IV. — THE MANUFACTURE OP GUNPOWDER. 



Automatic devices are arranged to drench the contents of 
buildings adjacent to a probable explosion. 

The diffusion of dust is avoided by boxing in those 
machines which produce it. 

Powder in barrels is always gently handled. It should 
never be rolled for transportation. 

These details are given to suggest the precautions neces- 
sary while handling gunpowder in service. 

PRINCIPLES OF THE MACHINES EMPLOYED IN THE MANU- 
FACTURE OF GUNPOWDER. 

Types. 

In order to derive the benefits of continuous operation, 
the tools yOX portions of the machines in contact with the 
material, are preferably of the rotary type. Reciprocating 
motion is objectionable, in that it wastes energy in revers- 
ing the direction of the motion at each end of the stroke. 

Classification. — The tools employed may be classified ac- 
cording to their functions, as follows: 





FUNCTIONS. 


NAME OP TOOLS. 


Nature 










of 
Operation. 




General. 


Special. 


General. Special. 








U.B011S \l^ 


continuous. 






fl. disintegration 


intermittent. 








{ 2. Barrels tumblins 


contnmous. 


1. 


To divide by 


. 




fl. cylindrical 


continuous. 






1 2. separation 


Sieves ■ 


2. flat 

1 


intermittent by 
reciprocating 
motion. 






fl. mixinff 


Batrels tumbling 


continuous. 


n. 


To combine by-j 

L2. pressure 


fl. rolling 
Th'^sjifin \ 2- thrusting 
Pi esses \ (hydraulic) 


continuous, 
intermittent by 
reciprocating 








motion. 


ni. 


To convey by 




Bands endless 


continuous. 



The rotary tools may be classified as to whether the 
material lies without or within the tool; as — 
1st. Rolls. 
2d. Tumbling or rolling barrels. 



IV. — TME MANU^ACTtrkE OF CtJNfOWDEft. 



Rolls. 

The object of a roller or roll is twofold. 

1st. To concentrate a given pressure on a small area of 
contact. 

2nd. To transfer this pressure to successive areas contin- 
uously. 

Relative motion between the material and the tool is, there- 
fore, necessary. 
Eeduction of Area. 

The reduction of area desired is generally attained by 
the curvature given to the smooth cylindrical surface of the 
roll; it may be increased by fluting the surface or by provid- 
ing it with pyramidal points. 

The effect upon a granular material then resembles crack- 
ing, rather than the crushing effect of the smooth roller. 
Transfer of Pressure. 

When the pressure is transferred but slowly, the parti- 
cles of the material may have time to adjust themselves in 
their new positions. The effect of the pressure will then be 
rather to condense the material than to disintegrate it by 
crushing. 
Eelative Motion. 

1. When the material is at rest, a single roller is used. 
Example: a rolling-pin. See fig. 8. 

In practice, the path of the roller is circular, so that its 
effects may be repeated. 

2. When the material moves, the rollers are in pairs and 
revolve on fixed axes in relatively opposite directions. Ex- 
ample: A clothes wringer. See fig. 14. 

In this case, they act but once upon the material, which is 
carried through them by friction, and fed to and removed 
from the rollers by its weight. 

To assist in feeding automatically, several pairs of rollers 
may be placed in tiers, surmounted by a hopper containing 



4 IV. — The manufacture op gunpowder. 

the material to be disintegrated. The upper tiers have the 
coarsest teeth and are placed farthest apart. 

A coffee-mill is a variety of this class. The rolls are ver- 
tical, concentric, and conical; the outer roll, which is fixed, 
being the more obtuse. The funnel-shaped space between 
them serves as a hopper, and as the material descends, pro- 
duces the effect obtained by the successive tiers above de- 
scribed. 

Fig. 4 shows a charcoal-mill and sieve. The roll is bal- 
anced to avoid excessive pressure. 

Barrels, 
Type. 

Tumbling barrels, as represented in fig. 5, are much used 
in the arts for abrasion. Their utility depends upon the 
inter-attrition of the contents. In powder making, besides 
the material, these often consist of balls, b, b, lifted by ledges, 
Z, Z, and continually falling back upon the material beneath 
them. 

When the operation has proceeded far enough, the door 
JD is removed, disclosing a perforated screen through which 
the finer portions may gradually escape upon the oscillating 
sieve, S. 

The product is collected in the drawer Z>/ 

Varieties. 

The nature of the barrel and of the balls varies with the 
explosiveness of the material and the character of the 
operation. Thus, the barrel may be of iron with iron balls 
where an inexplosive material is to be pulverized*; of a 
wooden skeleton covered with leather, using bronze or zinc 
balls, when the operation is dangerous; or covered with wire 



*When the material to be disintegrated is very tough, heavy iron 
cylinders are used instead of balls. 



IV. — THE MANUFACTURE OF GUNPOWDER. 

gauze netting, and using wooden balls, where simple com- 
minution of a friable material is desired. 

By omitting the balls and varying the size of the netting, 
such barrels may be used as sieves; and, by slightly inclining 
their axes to the horizon, both ends may be left open, when 
they will remove the dust. Fig. 4. 

If the barrels be tight and no balls be used, the contents 
will be merely polished. Such tools are much used in the 
arts for finishing the surface of rough metallic objects, and, 
in the manufacture of gunpowder, for glazing it. 

Mixing Barrels. 

Where simple mixture of the ingredients 'is sought, the 
barrel may contain paddles revolving independently upon 
its axle, as in a churn, fig. 6. The action of these paddles 
is also disintegrating, and, where time is important, may 
replace the more crude pulverizing apparatus described. 
Advantages. 

The principal advantage of the rolling barrels consists in 
their cheapness of construction and operation, by which 
their number may be multiplied, and the eifects of an 
explosion diminished. 

Carrying Bands. 

These are endless belts of a suitable width, which serve 
to carry continuously the material from one part of a 
machine to another. 

If horizontal, a plain band will suffice; but, if inclined, it 
is furnished with elevator buckets. Fig. 7. 

OPERATIONS OF MANUFACTURE. 

Processes, 
Nature. 

All the stages of manufacture may be referred to the 
following essential processes. 



b IV. — THE MANUFACTURE OF GUNPOWDER. 

1. Formation of a homogeneous press cake of required 
density. 

2. Breaking up the press cake into grains of required 
size and form. 

3. Finishing the grains so formed. 

Operations. 

The necessary operations may be divided into four 
principal groups, viz.: 

Jl. Pulverizing. 
2. Mixing. 
3. Moistening. 

II. Operations relating to press cake. ] \ p"ressi^n°^^^^"^' 
III. Operations relating to graining, -j \; gjf^/^^"^ 



IV. Operations relating to finishing. 



'1. Glazing. 

2. Drying. 

3. Dusting. 

4. Blending. 

5. Marking. 



X PRELIMINARY OPERATIONS. 

1. Pulverizing, 
Process. 

The nitre is generally in crystals that are sufficiently 
fine. Otherwise, this and the other materials are pulverized 
by any suitable process, either separately under single rolls 
or by a binary process in a barrel, viz.: the charcoal and 
sulphur together, or the charcoal and nitre together. 

Object. 

The pulverization should be thorough, so as to reduce 
the time required for incorporation ; the latter, owing to the 
cost of the plant and the smallness of the " charges " treated, 
is the most expensive of the operations. 



IV. — THE MANUFACTURE OF GUNPOWDER. 7 

2. Mixiftg. 

The three ingredients may be mixed by hand or in the 
rolling barrel. 

3. Moistening. 
Object. 

The object of moistening is generally to assist in the 
distribution of the nitre; to give consistency to the mass; 
and to prevent a dangerous rise in temperature during the 
various operations of manufacture. 

Limits. 

An excess of moisture may cause segregation of the 
nitre by crystallization, and its evaporation, as in store, may 
render the finished powder unduly porous. 

On the other hand, extreme desiccation may lead to the 
re-absorption of hygrometric moisture, which would affect 
the properties of the powder dried. 

The amount of moisture should never exceed 3 or 4 per 
cent. It is frequently renewed during manufacture, accord- 
ing to the state of the atmosphere and to the special object 
in view. The amount present is determined by desiccating 
a weighed sample. 

II. OPERATIONS RELATING TO PRESS CAKE. 

1. Incorporating. 
Object. 

This is intended to unite the dust of the ingredients as 
intimately as mechanical means permit, and thereby to facili- 
tate the conversion of the powder into gas. It is the most 
important of all the operations of manufacture. 

Process. 

The wheel mill (Figs. 8 and 9), used for this purpose, con- 
sists of two cast-iron cylinders Cy c^ weighing several tons 
each and acting as single rolls. 



b IV. — THE MANUFACTURE OF GUNPOWDER. 

In order that their effect may be exerted throughout the 
layer of composition, this is made only about one inch thick. 

The risk attending this disposition is diminished by fre- 
quent careful moistening, and by the eccentricity of the axle; 
this permits the wheels to rise and fall as obstacles are 
encountered. The constancy of the resulting pressure in- 
creases the uniformity of their effect. This arrangement is 
shown in Fig. 9. 

The arrangement of the wheels upon an axis rotating in 
a horizontal plane peculiarly adapts them to the require- 
ments of this operation. For, while both edges of either 
wheel have the same angular velocity, their paths described 
in the same time are notably different. Hence, it follows 
that the inner ed^e will tend to slide backward relatively to 
the outer edge; giving to the wheel a motion of rotation 
about an instantaneous vertical axis, combined with that 
about its permanent horizontal axis. 

The effect is to grind the material nearest to the centre 
more thoroughly than that nearest to the curb of the 
trough; because in the former case, the sliding of the wheel 
repeats the effect of its crushing, and, in the latter case 
replaces it in part. 

This effect is distributed by means of ploughs preceding 
the wheels, and by causing the wheels to travel in different 
paths. 

The process takes about two hours, depending on the 
quality of the product; it continues day and night, while 
that of the other machines is confined to daylight. 

Product. 

The product of the wheel mill, called mi7/ cake, unless 
consolidated by very slow rolling, is friable and of variable 
thickness and density. These defects are corrected by the 
next process. 

The perfectness of the incorporation may be tested by 



IV. — THE MANUFACTURE OF GUNPOWDER. 9 

flashing a small quantity upon a glass plate. No residue 
should be left. The stains left by flashing powder on the 
blue paper used in solar printing are characteristic, and 
increase the delicacy of the test. 
Variations in Process. 

In case of necessity the incorporation may be less 
perfectly performed by the stamp mill (Fig. 13), or by the 
protracted use of the rolling barrel. (See also page 15.) 

2. Pressing, 
Object. 

The object of pressing powder is to increase its density 
as a fuel, and to give it sufficient hardness to resist the 
formation of dust in transportation. 
Kind of Press. 

The intensity and uniformity of the pressure required 
usually demand the action of an hydraulic press, Fig. 10; 
although, when quantity rather than quality is desired, 
single or double rolls may be employed. 
Process. 

To increase the uniformity of the material pressed, the 
product of the various wheel mills is coarsely granulated 
and mixed. Then, having been moistened, it is placed in 
layers between plates which are kept at about two inches 
apart until the spaces between them are filled. 

The powder is then gradually compressed to about half 
its former volume; being kept from spreading by hinged 
side pieces, which, being latched together, form a sort of 
box. This box is generally vertical, but for convenience is^ 
preferably horizontal and on the level of the floor. 
Variations in Density. 

The resulting density increases within limits, with the 
duration of the pressure and with the amount of trituration 
which the powder has received. The proportion of mois- 



10 IV. — THE MANUFACTURE OF GUNPOWDER. 

ture largely affects the density, since it acts as a lubricant 
between the particles. The density is not uniform through- 
out the press cake, being always greatest next to the mov- 
ing surface. 

To obtain uniform density, upon which it will be seen 
that the uniform action of powder greatly depends, one 
must compress equal masses equally incorporated and con- 
taining equal quantities of water at equal rates into equal 
volumes. 

Wiener's Powder. 

These requisites are with difficulty attained, owing to the 
variable hygrometric condition of the atmosphere. It has 
been attempted to dispense with water for pressing, by 
heating the powder during this operation slightly above the 
melting point of sulphur. 

This process, invented by Colonel Wiener, of Russia, 
renders the gunpowder practically waterproof. 

Effect of Form of Plates. 

The plates between which the powder is pressed are gen- 
erally flat, in which case the press cake comes from the press 
in slate-like slabs. The powder, resulting from breaking up 
these cakes, is called of irregular granulation^ or simply 
grained powder. 

Modern powders for heavy guns are often pressed be- 
tween plates, the surfaces of which are regularly indented 
or ribbed after the manner of a waffle iron (Figs. 11, 12). 
The resulting press cake may be readily broken up into 
grains of great uniformity of size and shape. Such powders 
are said to be of regular granulation. 

Molded Powder. 

When the press cake is made exceedingly small, so that 
each cake shall make one grain, the powder is said to be 
molded. See molded J>rismatic, Figure 12. 



IV. — THE MANUFACTURE OF GUNPOWDER. 11 

Such powders are made by a number of properly shaped 
punches and dies simultaneously operated. Fig. 15, post. 
Concrete Powders. 

The structural homogeneity of the product depends 
much upon the condition of the material compressed. If 
the soft mill cake, above referred to, be replaced by that 
which has already been pressed and granulated, a co7icrete 
powder is produced; the fine grains composing it being 
cemented together by the pressure into a mass, the 
porosity of which is greatest in the middle. The burning 
of this powder is notably different from that of the homo- 
geneous mass generally produced. 

OPERATIONS RELATING TO GRAINING. 

Object. 

The object of graining, like that of splitting fire wood, is 
to increase the initial surface of combustion. 
Operations. 

The press cake is broken up by a series of rolls (Fig. 14), 
and sifted between limiting sieves. 
Principle of Gauging. 

The use of these sieves illustrates a principle common in 
manufactures; this principle when it is applied tp individual 
articles, is called gauging. 

Assuming that no two objects can be made of precisely 
the same size, a certain tolerance is established by the 
adoption of a maximum gauge, through which each object 
must pass, and of a minimum gauge, through which no ob- 
ject may pass. 

The grains which are too coarse or too fine are reworked. 

Special Operations in Graining, 

Regular Granulation. 

These depend upon the kind of grain required. For 



13 IV. — THE MANUFACTURE OF GUNPOWDER. 

example, the powders of regular granulation require only 
breaking up as by hand. 
Pebble Powder. 

The English cubical, or pebble powder is made by cutting 
the flat press cake into prisms between ribbed rolls, and 
then recutting these prisms across their length. 
Flat Powder. 

The flat French powder (Castan's) is made by roughly 
breaking a rather thin press cake, so as to make the thick- 
ness of the cake the minimum dimension of the finished 
grain. (Fi^. 12.) 

IV. — OPERATIONS RELATING TO FINISHING, 

1. Glazing, 
Object. 

The object of glazing is to remove the angles and asper- 
ities of the grain; these would form dust in transportation 
and facilitate the absorption of moisture in store. 

It compensates for the diminished density of the interior 
of the press cake from which most of the grains are formed, 
by increasing their superficial density by their mutual col- 
lision; it also increases the homogeneity of their struc- 
ture by the heat which is thus evolved. 
Process. 

Moisture having been added to give some plasticity, the 
grains are rolled in a wooden barrel without balls. 

2. Drying, 
Object. 

The object of drying is to reduce to normal limits, the 
moisture required in the previous stages of manufacture. 
Process. 

It is accomplished by passing a current of warm, dry air 
through successive layers'of powder spread on screens or 
on shallow trays. 



IV. — THE MANUFACTURE OF GUNPOWDER. 13 

The temperature should be increased gradually, to avoid 
disintegration of the grains. 

3. Dustiftg, 
Object. 

This is intended to remove the dust resulting from the 
glazing, and detached from the surface of the grains by 
drying. 

4. Blending, 
Object. 

To neutralize unavoidable variations in manufacture, 
powders of the same size and nature may be blended so as 
to give certain average results. 
Process. 

Fine grain powders are mixed according to their densi- 
ties, and those of larger grain, according to their ballistic 
properties. Molded powders are blended in charges, grain 
by grain alternately. 

6. Marking, 
In the U. S., powders receive certain conventional fac- 
tory marks, of which the first two letters generally relate to 
the size and use, and the final letters to recorded variations 
in the manufacture, or to the date at which certain lots are 
made. Thus, I. K. A. might mean the first lot of I. K. 
powder used for field guns; E. V. B. the second lot of 
hexagonal powder for sea-coast guns, etc. Similar symbols 
are used abroad and are very convenient. 

VARIATIONS IN MANUFACTURE. 

COCOA POWDER. 

History. 

The most important improvement in gunpowder, since 
1860, is the invention by the Germans of what, from its 
color, is called cocoa or brown powder. 



14 IV. — THE MANUFACTURE OF GUNPOWDER. 

It is notable for being the first important modification of 
the long established composition of gunpowder which has 
proved practically successful, and, as will be seen, for the 
paradoxical nature of its results. In this country it has so 
far been used only in heavy cannon. 

Characteristics. 

As made in this country by the Du Pont Powder Works, 
it differs from ordinary powder; — 

1. In the composition of the charcoal, which is made by 
steam heat, as described Chap. III. 

2. In the addition during incorporation of gummy carbo- 
hydrates, such as sugar, dextrine, etc. 

3. In the proportion of the ingredients — 

Nitre, 81.5 per cent. 

Charcoal and Carbo-Hydrates, 15.5 
Sulphur, 3. 

lOOO" 

4. It is difficult to ignite, requiring in the gun a few 
prisms of black powder to be built into the cartridge near 
the mouth of the vent. 

6. When ignited, unconfined, it seems to/j/j^^rather than 
to deflagrate explosively. 

This and its want of friability make it safe to transport 
and handle in store. 

6. It is quite hygroscopic, but suffers less from moisture 
than black powder. 

7. Its ballistic properties are extraordinary, 

8. It gives comparatively little smoke. 

Manufacture. 

This resembles that of all the molded concrete powders. 
The grams compressed are of the size of mortar powder, 
and are slightly moistened before pressing. 



TV. — THE MANUFACTURE OF GUNPOWDER. 15 

Press for Molded Powders. 

Pressing is done by carefully regulating the motion of the 
plungers of a duplex hydraulic press, which molds about 
100 prisms at a time. 

In fig. 15, ^ is a fixed mold plate containing a number of 
apertures of a cylindrical or prismatic form, into which the 
perforated plungers, G^ Z, fit. 

Through the axes of the plungers run needles, H, sim- 
ultaneously operated by the toggle-joint, /, and the supple- 
mentary cylinder, K. 

A quantity of powder is swept into the apertures, X^ until 
they, are full. The rams, B^ B' , then approach each other 
with equal velocities; and as L enters E, ZT rises into L. 

After suitable pressure, L rises; ZT is withdrawn, and G 
rises; lifting the prism so that it may be swept off into a 
box. 

The resulting prism has very dense ends, separated by a 
somewhat porous belt. 

NORDENFELDT POWDER. 

Object. 

To increase the intimacy of the incorporation and to 
avoid the danger of performing it by mechanical means. 

Manufacture. 
Charcoal. 

Straw or cotton-wool is carbonized by exposure to a 
stream of gaseous HCl. 
Sulphur. 

Dissolved in CS^ and added to Charcoal. 
Nitre. 

In aqueous solution is gradually added to above. 

The mass is mixed by paddles while in a liquid state, 
after which the vehicles are distilled and evaporated. The 
usual operations following incorporation are then pursued. 



V. — INTERIOR BALLISTICS. 



CHAPTER V. 



INTERIOR BALLISTICS. 

Division of Ballistics. 

Ballistics, which treats of the motion of projectiles, is 
divided into interior and exterior ballistics, according as 
the motion of the projectile within or without the gun is 
considered. 
Interior Ballistics. 

The latter science is studied later in the course; but the 
former is so intimately related to the conversion of gun- 
powder into gas, that it is expedient to deal with it while 
the circumstances of this conversion are fresh in our minds. 
The Gun as a Machine. 

Functionally speaking, the gun is a machine by which the 
potential energy of the gunpowder is converted into the 
kinetic energy of the projectile. 

It is well to consider in advance certain elementary prin- 
ciples relating to the construction of this machine and to 
the measurement of the energies received and usefully 
converted. 

FORM OF GUN. 

strength vs. Weight of Guns. 
It will hereafter appear that, 
considering a gun to be com- 
posed of a series of elementary 
concentric cylinders, the resist- 
ance which each of these cylin- 
ders offers to a permanent tan- 
gential deformation varies in- 
versely with the square of its 
radius; or, if S represent the 
stress, ABy on the interior cir- 




tJ^IVE 



"\ 



O^' 



.-f*\ 



V. — INTERIOR BALLISTICS. 



cumference of an elementary area of cross section of the 
bore, the radius of which is r j and y be the stress from the 

same cause at any other radius, x; then j* = — ^ . This is ex- 

00 

pressed by figure 1. 

But the weight of the elementary longitudinal cylinders 
increases with the square of their radii. 

It therefore appears, that after a certain point, an increase 
in the thickness of the walls of the gun adds rapidly to its 
weight and but slowly to its strength. 

Strength vs. Cost. 

Also, when the diameters of cannon exceed a certain 
limit, the difficulties of construction attending an increase 
in diameter, increase much more rapidly than do those at- 
tending an increase in length. 

Conclusion as to Form of Gun. 

A given amount of energy may, therefore, be most 
economically transferred from the gunpowder to the pro- 
jectile, by diminishing the rate of transfer and increasing 
its duration. 

Considerations relating to the weight and cost of a given 
cannon having thus determined the most suitable diameter, 
it should be kept constant for the entire length of the gun, 
provided that the stress to which it is exposed shall also be 
constant. 

It is the object of recent improvements in guns, powder, 
and projectiles, to make this stress as high as it is safe, and 
to prolong it as far as possible throughout the length of the 
bore. 

Recent changes in the profile of cannon illustrate the 
progress which has so far been attained toward realizing the 
conditions of this ideal gun. 



-INTERIOR BALLISTICS. 



FORM OF PROJECTILE. 

Until quite recently, all but experimental cannon were 
muzzle loaders. 

Until about 1860, they were smooth-bores and fired 
spherical balls. 

The success of the rifled field pieces in the war between 
France and Austria led to the general use of projectiles, 
oblong in shape, but, like the spherical projectiles, smaller 
than the bore. 

These cannon have been recently replaced by rifled 
breech loaders, firing projectiles provided with a compres- 
sible ring slightly greater in diameter than the bore. 

The enlarged chamber, which this form of projectile re- 
quires, and the resistance which it offers to motion, consid- 
erably modify the circumstances of the conversion. 



Note. — This chapter is introductory to the seven following chapters. 



VI. — VELOCIMETERS. 



CHAPTER VI. 

VELOCIMETERS. 

Object. — In order to study experimentally the transfor- 
mation of energy from the gunpowder to the projectile and 
to the gun and carriage, and to measure the kinetic energy 
residing in the projectile, both as it leaves the gun and when 
it has done work upon the medium through which it passes, 
special instruments, known as velocimeters^ chronographs^ 
chronoscopes, etc., have been devised. 

Importance. — Except where otherwise specified, the fol- 
lowing discussion relates to the means employed for meas- 
uring the initial velocity of the projectile. This is the great 
measure upon which all ballistic predictions are based. 

Constituent Parts. — All such instruments are chronometers 
and consist essentially of a register and a marker. 

The register has a known velocity relative to that of the 
marker and receives from it a succession of marks, the 
time equivalents of the spaces between which measure the 
periods between certain events. 

The events are the first visible effects produced upon the 
velocimeter by the arrival of the projectile at certain 
epochal points. These are often targets. 

Signal Time. — The interval between an epoch and the 
corresponding event is called the time of transmission, or 
the signal time. See figure 14. 

The time from any origin to an event = time to the 
epoch, /, + signal time, G\ and the interval between two 
events, 8 =(/" + a") - {t' + 6')^{t" -f) + (a' - c'). If 
G''-a'=Oj t'-t', or r, =d. If a"-a'=Cj r=d-C; if 
•then r=0, d--C. To diminish accidental variations in C, 
a is made as small as possible. Knowing s, the distance 
between the epochal points, and r, the mean velocity of the 
projectile over the intervening path may be determined. 



VI. VELOCIMETERS. 



Functions of Velocimeters. — Conceiving times and dis- 
tances as being each measured from common origins, we 
may say that the instruments record differences in instru- 
mental distance corresponding to differences in time, 
which differences in time correspond to differences in dis- 
tance of the projectile from any point upon its trajectory. 

Classification. — The velocimeters may be divided into 
three general classes according as they are adapted to 
record: — 

I. One difference in time corresponding to one definite 
difference of distance of the projectile from a common 
origin. 

II. Successive differences in time corresponding to sev- 
eral successive definite differences of distance of the pro- 
jectile from a common origin. 

III. Continuous differences in time corresponding to con- 
tinuous differences of distance of the projectile from a com- 
mon origin. 

Comparison of Classes. — For each fire the instruments of 
class I determine the mean velocity of the projectile between 
one pair of points. 

Those of class II determine that between several succes- 
sive pairs of points. 

Those of class III set forth continuously the circumstances 
of the motion. 

By taking the epochal points at constant intervals, either 
of distance or of time, the indications of the instruments of 
class II may, by interpolation, serve to determine the varia- 
tions in velocity corresponding to known values of A J or A r 
and thus to approximate to the law of motion more fully 
expressed by the record of instruments of class III. 

This method enables the epochal points to be separated 
further than the construction of the instruments of class III 
permits. 



VI. — VELOCIMETERS. 



CLASS I. 

Events.— In class I the events are those of the falling of 
certain masses, either freely or with constrained motion. 

The position of the marks indicates indirectly the interval 
of time separating the events. 

Operation. — Calling the masses respectively a and b, ac- 
cording to their priority of fall, b is caused to strike a while 
a is falling. The problem resolves itself into determining 
the difference between two intervals of time, viz.: 

4=how long a was falling before it was struck. 

/b=how long it took b to strike a. 

Then 4— 4=0=time that a was falling before b started 
to strike it=:the interval between the starting of a and of b^ 
which is the time interval required. 

a and b are generally caused to fall by the demagnetiza- 
tion of electro-magnets in separate circuits, which are broken 
by the arrival of the projectile at the epochal points. Or 
they may be made to fall by the cutting of taut threads by 
which they have been suspended. 

Disjunctor. — An essential appendage to machines of this 
class is the disjunctor^ by means of which, both circuits being 
simultaneously broken, the masses a and b are caused sim- 
ultaneously to fall. 

EXAMPLES OF CLASS I. 

1. THE BENTON VELOCIMETER. 

See figures 1, 2 and 3. 

Description.— This instrument, devised by the late Colo- 
nel J. G. Benton, the first Instructor of Ordnance and Gun- 
nery at the U. S. Military Academy, employs either elec- 
tricity or threads to support a and b. These are similar 
pendulums suspended at the centre d of the arc b c a so 
that they are constrained to oscillate in adjacent planes par- 
allel and close to the face of the arc; this arc, being gradu- 
ated, forms the register. 



VI. VELOCIMETERS. 



That pendulum which lies nearest to the arc carries at its 
outer end the marker; this is a delicate bent lever pivoting 
in a plane perpendicular to the arc, and so placed that its 
inner end, which is lightly covered with printing ink, shall 
travel close to the register. 

As the pendulums pass each other, a projection on tb.e 
inner face of the outer pendulum strikes the outer end of 
the marker and causes it to indicate the point of meeting as 
at c^ figure 2. 

Inspection of the figure shows 0=4 — 4=time of passage 
over the arc a o c^ minus time of passage over the arc b ^:=2X 
time of passage over the arc o c. 

Disjunctor. — The disjunctor in this instrument serves to 
determine C, the difference in signal times. 

It consists of two flat steel blades, mn, ni'n', secured to 
the base at m^ 7n' ^ and having their free ends, n^ «', resting 
upon posts ^, b'^ through which and the blades the electric 
current passes. 

Between the blades is a powerful bent spring r, provided 
with a cross piece p q, which lies beneath the blades and 
lifts them when the spring is released from the latch g. The 
button Sy having been pressed, contact is made; it is broken 
by pinching the latch. 

Determination of Time Value of Record. — To determine 
the time corresponding to a given reading, let / be the 
length of the equivalent simple pendulum ; v the velocity of 
the center of oscillation or point b; y the vertical distance 
passed over by this point; x the variable angle which the 
axis of the pendulum makes with the vertical; and t' the 
time necessary for the point b to pass over an entire circum- 
ference, the radius of which is /, with a uniform velocity v. 
We then have : 



V=: 



y/2gy. 



VI.— VELOCIMETERS. 



Substituting for y its value in terms of x, the above ex- 
i:)ression becomes : 

^=V2^^"7cos^ 
from which it is evident that the velocity of the pendulum 
increases from its highest to its lowest point. 

The time /' is equal to the circumference of the circle, 
the radius of which is /, divided by the velocity v; if this 
value of f be again divided by 360, we shall have very 
nearly the time of passing over any degree at the height y^ 
or — 

2 7tl 



t= 



360^2^/ cos ^. 



Calling /" the time of a single vibration of the pendulum 
of the machine, we have by known laws — 

Substituting this value in the equation above, and represent- 
ing— 

jg^|by«, wehave 



V COS X. 

To determine /", the pendulums are removed from the 
machine, and the cylindrical journals about which they re- 
volve are replaced by others, the bearing surfaces of which 
are knife edges. Each pendulum is started vibrating through 
a very small arc. By means of a stop-watch the time of 
1,000 vibrations may be found. By repeating the operation 
several times and taking the mean, the time of a single 
vibration may be determined very exactly. This time for 
pendulums of recent construction is 0.378 of a second. 



VI. — VfiLOClMETERS. 



If now X be made successively equal to 1°, 2°, 3°, &c., 
and the corresponding values of / be found, we shall have 
the time of passage of the pendulum over each degree. 

By adding the time of passage over the first degree to 
that over the second, we shall have the time of passage 
over an arc of 2°. In the same manner, by adding this 
latter time to that over the third degree, we shall have the 
time of passage over an arc of 3°, and so on. 

The following table has been determined in this manner: 
Table. 



De- 

grefeB. 


Time in seconds 

of passage over 

each degree. 


Sum of times in 
seconds. 


De- 
grees. 


Time in seconds 

of passage over 

each degree. 


Sum of times in 
seconds. 


1 


.00148504 


.00148504 


19 


.00152749 


.02849909 


2 


.00148538 


.00297042 


20 


.00153174 


.03003083 


3 


.00148594 


.00445636 


21 


.00153684 


.0315676T 


4 


.00148673 


.00594309 


22 


.00154213 


.03310980 


5 


.00148775 


.00743084 


23 


.00154772 


.03465752 


6 


.00118001 


.00891985 


24 


.00155361 


.03621113 


7 


.00149019 


.01041034 


25 


.00155980 


.03777098 


8 


.00149221 


.01190255 


26 


.00156630 


.03933723 


9 


.00149415 


.01339670 


27 


.00157313 


.04091036 


10 


.00149033 


.01489303 


28 


.00158029 


.04249065 


11 


.00149876 


.01639179 


29 


.00158780 


.04407845 


12 


.00150142 


.01789321 


30 


.00159565 


.01567410 


13 


.00150433 


.01939754 


31 


.00160388 


.04727798 


14 


.00150749 


.02090503 


32 


.00161248 


.04889046 


15 


.00151089 


.02241592 


33 


.00162147 


.05051193 


16 


.00151455 


.02393047 


34 


.00:63087 


.05214280 


17 


.00151847 


.02544894 


35 


.00164070 


.05378350 


18 


.00152266 


.02097160 


36 


.00165092 


.05543442 



To Compute a Scale of Velocities. — It should be rem.em- 
bered that the times above determined correspond to but 
half the difference of the arcs described by the two pen- 
dulums; therefore, they should be doubled in order to get 
the time r. 

2. THE LE BOULENGE CHRONOGRAPH. 

See Figures 4, 5, 8, 9. 
Description. — This velocimeter, invented by Captain Le 
Boulenge of the Belgian artillery, is the one used generally 
throughout the world for the determination of initial 



Vt. — vfiLO^iMETERg. 



velocities. In it the masses a and b are rods falling 
freely from electro-magnets E, E' . These are supported 
on a stand s, so placed that while a may fall through the 
foot of the stand, the fall of b is arrested by a trigger /, 
the shock upon which releases a knife-shaped marker m. 
The edge of this marker lies close to the path of a, so that 
a very slight movement of it to the right, under the impulse 
of a powerful spring which is liberated by the fall of b^ 
produces a mark upon that elementary circle of a which 
was opposite to 7n at the moment of impact. 

Disjunctor. — Although the operation of the disjunctor is 
the same as with the Benton velocimeter, its object in the 
LeBoulenge instrument is quite different. 

It serves, by making r=(9, to determine the value of 4* 
since then 4=4> o^^ the time that a was falling before it 
was struck measures the time required for b to strike it. 

This instrument does not serve to determine the signal 
time, but it may be shown that if the difference in signal 
times remains constant the time recorded between the 
events = time between the epochs, or 0=?. 

Operation. — This mark may be made in three ways, as 
follows: 

1. Release m while a is at rest; the mark will fall at O, 
which is the origin for future measurements. 

2. By means of the disjunctor, rupture E and E' simul- 
taneously; the mark will be at some point Z> at a height h 
above O, corresponding to the time required for b to fall to 



m and for m to mark the rod a. This time is /, 



1 1h 



or the time required for b to strike a. The mark D is 
called the disjunction mark. 

3. Use as Megagraph. — Rupture E and immediately 
afterward E'\ the mark will occur, as at R^ at a height /%' 
above O. This is the usual case in practice. Then 



VI. — VELOCIMETERS. 



•v 



2 h' 

= the time during which a was falling before 

i 

it was struck, and t^—t^=Q^ as with the Benton velocimeter. 
The mark R is called the record mark. 

As a matter of convenience only, the construction of the 
instrument permits 4 to be made constant =0^ 15, so that 
a rule may be so graduated, that, for a given interval be- 
tween targets, the velocity corresponding to a height OR 

s s 

may be obtained by simple inspection, for v =—= 

T 4-OM5 

The instrument so arranged is called a Megagraph. 

(Greek ^eya8,-great.) 

Use as Micrograph. — By raising E' so that the lower 
end of b may be nearly level with the top of a, D will be 
made to occur near that section of a which passes m with 
the greatest velocity. This serves to verify the accuracy 
of the operation of the disjunctor, of the magnets, and of 
the marking apparatus; since, if these parts worked with 
perfect uniformity, successive disjunction marks would be 
found at the same height above O. The velocity of a at 
the moment of marking magnifies the visible consequences 
of deficient uniformity and assists in correcting the causes 
to which it is due. 

With this arrangement, if b is detached before a^ the 
mark will be found as at R and Q=t^—t^. 

The advantages of this arrangement for the measure- 
ment of very small intervals of time give it the name of 
micrograph. (Greek fxiupoB^-smali.) 

Determination of time limit. — The following reasoning 
determines the circumstances under which the instrument 
should be used as a megagraph, or as a micrograph. 

Considering for the moment 0r=r and remembering that 
we are measuring the interval t=- we see that, with the in- 

V 



VI. — VELOCIMETERS. 



strument arranged as a megagraph, r may be greatly dimin- 
ished by increasing v and reducing s. The mark R will then 
be made near D where a has but little velocity, and therefore 
imperceptible differences in h may correspond to considerable 
differences in r and hence in v. Since the instrument was 
invented, initial velocities have increased from 1,200 f. s. to 
over 2,000 f. s. while s may be restricted, as at West Point, 
so as to be reduced from 50 metres (164 feet, for which interval 
the instrument was made) to but 50 feet and even less. 

On the other hand, when using the instrument as a 
micrograph, if r increase unduly, the mark will occur in 
the same neighborhood as before, and the same conse- 
quences will ensue. 

It becomes therefore necessary to determine a common 
time limit within which the instrument should be used as a 
micrograph and beyond which as a megagraph. 

For this time the mark will, in both cases, occur at the 
same height above O. For the megagraph, it will be at 
the height corresponding to 4=r + 0^''*'-.15. 

For the micrograph, since the length of ^=about 0.5 
metre, the maximum value of /b=:0^®*^-.32; therefore, 4= 

Qsec.32_2'. 

Equating these two values of 4, we have r=0.^®^085 as 
the value of the time limit. 

Details of the Instrument. 

Chronometer. — Referring to the definitions, p. 1, the 
rod a is seen to be a register^ the time of fall of which to 
any distance h below the edge of the knife making the 
mark (9, is known. 

This rod in this instrument is called the chronometer. It 
is enclosed by a tightly fitting zinc tube which receives the 
marks. By turning this tube axially, and finally by revers- 
ing it, many records may be made before it need be changed, 



10 VI. — VELOCIMETERS. 



Registrar. — The rod b is called the registrar. It is much 
lighter than a. 

Adjustment. — To diminish differences in the time of de- 
magnetization, the power of the magnets, E, E\ is reduced 
to a safe minimum, which, by the movable screw-cores con- 
tained in the magnets, is determined as follows: — 

A definite surplus of power* is assured by attaching to 
each armature a make-weight in the form of a tube of -^ 
the weight of the armature. The weighted armature having 
been suspended from the magnet, the core of the latter is 
slowly unscrewed until the armature falls. The make- 
weight is removed before the armature is again applied. 

Disjunction Circle. — When it is desired to read velocities 
directly from the rule, the value of t^ is made constant by 
varying the height of fall of b so that the mark shall fall 
upon a disjunction circle previously traced upon the zinc 

recorder at a height above O = ~ — ^ — • 

Levelling. — The instrument is levelled by using the sus- 
pended chronometer as a plumb, 
between the epochs. 

Bregers Improvemen'.s. — In order to diminish variations 
in o'a— o'b resulting from variations in the method of rupture, 
depending upon whether the circuit is broken by the dis- 
junctor or by impact of the projectile on the target wires, the 
improvements of Captain Breger of the French service 
tend: — 

1. To diminish differences in the time and velocity of 
rupture of the two circuits by the disjunctor, which differ- 
ences are due to the unequal operating of the parts of the 
disjunctor. 

Such differences are found to make material differences 
in the times required to demagnetize E, E', in consequence 
of variations in the intensity of the induced currents follow- 
ing variations in the method of rupture. 



VI. — VELOCIMETERS. 11 

2. Differences in the rate of demagnetization have been 
avoided by making as nearly equal as possible the masses 
a and b, and therefore the magnetic states of E and E'. 

These and other minor mechanical improvements have 
diminished the mean error to ^ of that form.erly found. 

CLASS II. 

Register. — The register in these instruments generally 
consists of a revolving polished metallic cylinder, the angu- 
lar velocity of which is known. The surface of the cylinder 
is preferably smoked, so as to make visible the marks which 
it receives. 

Marks. — The marks are made in two general ways; — 

1st. By the trace of a quill point held lightly against 
the cylinder. 

By giving the quill point relative longitudinal motion 
during the rotation of the cylinder, the trace may be 
greatly developed helically. 

This trace being developed during the motion of the 
projectile, the latter's arrival at an epochal point may be 
signalized by a sudden motion of the quill point along a 
rectilinear element of the cylinder, causing a jog or offset 
in the trace. See Fig. 6. The offset is here the mark. 

This motion may be caused by the action of a spring 
previously in equilibrium with the attraction of an electro- 
magnet. This magnet is included in a circuit that is broken 
by the arrival of the projectile at the epochal point. 

If the circuit can be re-established before the next 
epochal point is reached by the projectile, the quill point 
will return to the prolongation of the trace, and one quill 
point will suffice. Otherwise, as in Fig. 6, as many quill 
points and circuits are needed as there are epochal points. 

3nd. The mark may result from the passage of an 
induced electric spark caused by the rupture of a primary 
circuit at each epochal point. 



13 VI. — VELOCIMETERS. 



Signal Times. — In order to avoid variations in the time 
of signaling, it is advisable, in both cases above cited, to 
include all the epochal points in the same circuit and to 
provide each of them with the means of renewing the 
broken circuit automatically before the projectile can arrive 
at the next point. See Targets, Class II, below. 

When the times to be measured are exceedingly minute, 
this may not be feasible. Equality in signal times is then 
sought by increasing the delicacy of the apparatus and 
is verified by the simultaneous rupture of as many circuits 
as there are markers to be operated. 

Tuning Fork. — Uniformity in the rotation of the cylinder 
is either assumed from the accuracy of the apparatus or 
may be neglected by attaching a tracing quill to one of the 
tines of a tuning fork, the time of vibration of which is 
known. 

The trace then takes the form of a harmonic curve, the 
alternate intersections of which with a median trace, formed 
when the fork is at rest, mark the ends of each double 
vibration of the fork. 

The duration of the double vibration is the unit of 
measure of time; if the velocity of the surface upon which 
the trace is formed be constant during any double vibration, 
fractional parts of the intercepted median line will measure 
corresponding portions of the unit of time. 

The double vibration, instead of the single vibration, is 
selected as the unit in order to neutralize errors of meas- 
urement. The median line gives the most definite inter- 
sections with the harmonic curve. 

Interrupter. — When the total time of the observation re- 
quires it, the vibrations of the fork F, Fig. 7, may be sustained 
by the use of adjacent electro-magnets, w, w, the attrac- 
tion of which separates the tines, /, t, until the rupture of the 
circuit through the spring R^ releases them. The spring is 



VT. VELOCIMETERS. 



13 



used instead of a rigid contact so as to prolong the influ- 
ence of the magnets. The reaction of the fork due to its 
elasticity renews the circuit and makes the process con- 
tinuous. 

This device, as applied to the Schultz Chronoscope, is 
known in this country as the Russell interrupter. It is due 
to Captain Russell of the Ordnance Department. 

When the total time of vibration is very short, no inter- 
rupter is required. In this case the fork may be set vibrat- 
ing by the sudden withdrawal of a wedge inserted between 
its tines; it is then abandoned. 

CLASS III. 

In instruments of this class relative motion is given to 
the register directly by the motion, either of the piece or 
of the projectile. 

The velocity of the register at any portion of its path is 
determined by tracing upon it a harmonic curve with the 
tuning fork, or by giving it a known velocity at right angles 
to that of the moving part. In either case, a compound 
curve is traced from which the required relations between 
space and time may be deduced. 

Examples: — 

If to a gun about to recoil be fastened a bar upon the 
smoked surface of which the harmonic curve is traced dur- 
ing the recoil, or if some point of the gun be kept in con- 
tact with a cylinder rotating at a known velocity about an 
axis parallel to the direction of the recoil, we may in 
both cases determine by interpolation the velocities desired: 

For example: — 



Travel 


Time. 


A/ 


A X 


ft. 
0.00 
0.02 

0.04 


sec. 
0.0000000 
0.0018182 
0.0023772 


sec. 

0.0018182 
0.0005590 


f. S. 

11.0 
35.8 



14 VI. — VELOCIMETERS. 

Knowing thus the mean velocities between many pairs 
of epochal pjints, it is possible by interpolation to deter- 
mine the accelerations at each of the epochal points and, 
knowing the mass of the moving object, to determine the 
intensity of the pressure accelerating it. 

TARGETS. 

CLASS I. 

The epochal points are generally wire screens stretched 
across the trajectory, as shown in Fig. 9. 

Cannon. — In order to prevent injury to the first screen 
and to allow for the acceleration of the projectile for a 
short distance after it has left the muzzle, due to the rela- 
tively great velocity of the escaping gas, the first screen is 
put at a distance from the muzzle, which increases with the 
calibre of the gun. 

When they are situated in the bore of the gun, as in Cap- 
tain Noble's experiments, Figs. 11 and 12, the wire may be 
severed by the action of a wedge raised by the passage of 
the projectile. This arrangement requires the walls of the 
gun to be pierced radially as many times as there are 
epochal points. 

To avoid this piercing, the L^tard apparatus. Fig. 10, is 
devised. It is principally of wood, cemented by resin to 
the surface of the bore. The head ot the metaUic bolt, a, 
and the metallic washer, b, are held in contact by the cross 
pin, c. The impact of the projectile on the point of a breaks 
the circuit and sweeps the fragments out to the front. 

Small Arms. — For small arms, in order to save the time re- 
quired in repairing at each fire the distant target, it consists 
of an iron plate having attached to its back a flat elastic 
blade, through which the circuit passes as in the disjunctor, 
Fig. 3. The shock of impact breaks the circuit which is 
immediately re-established by the elasticity of the blade. 



VI. — VELOCIMETERS. 15 



CLASS II. 

Instruments of this class that use but one circuit for all 
the targets have an arrangement, shown in Fig. 13. 

The weights, IV, depress the free ends of the spring wire 
staples, df d, f, so that the current may pass from the brass 
plate, ay to the brass plate, <r, through the staple, bj and from 
^ to ^ through d, and so on. 

When one of the threads / is broken by the projectile, 
the free end of one of the tines of d flies upward, break- 
ing the circuit for an instant, but renewing it as soon as the 
upper side of the oblong hole in c is reached. 

The West Point target, figure 15, resembles that above 
described, but is applied to instruments of Class I. 

A discontinuous copper strip, c, c, c, conveys the current 
when the flanged copper tubes /, t (cartridge cases), are drawn 
into place by the weights w, w. 

When a weight is cut the spring, s, lifts its tube and the 
circuit is broken. 

Compared with fig. 9, the advantages are — 

1. The circuit is broken in the same manner, both by the 
disjunctor and by the projectile. See page 10. 

2. The tension of the threads and the resistance of the cir- 
cuit are more constant than when a spHced, continuous target 
wire is used. 

3. The targets are more readily mended, and the " short 
circuiting " of leading wires by fragments of the target wires 
is avoided. 

ELECTRIC BATTERIES. 

These should be as constant as possible. Where storage 
room permits the employment of a large number of elements, 
the batteries of the gravity type are preferred, except for pro- 
ducing the sparks referred to on page 11. 



VII. — PRESSURE GAUGES. 



CHAPTER VII. 

PRESSURE GAUGES. 
Object. 

From the circumstances of the case the transfer of energy 
from the gunpowder to the projectile is accompanied by a 
considerable elastic pressure upon the walls of the gun, 
the effects of which, to be guarded against, require the 
intensity of the pressure to be known. 
History. 

Owing to the want of suitable apparatus, pressures were 
formerly inferred only from the injury resulting to the gun, 
and it was not until the time of Rodman that this important 
requisite was supplied. Since then great improvements have 
been made, some of which will be described. 
Nature of Pressure. 

The pressure varies at each instant during the passage of 
the projectile through the bore, and is generally taken to be 
constant throughout the volume in rear of the projectile at 
any point of its path. If we adopt Noble's hypothesis, 
hereafter to be explained, this is equivalent to saying that 
the gases in rear of the projectile at any instant are of uni- 
form density. 

But the expansion to the front and rear, in consequence 
of the motion of the projectile and of the piece, diminishes 
the density of the successive layers, estimated in both direc- 
tions from that layer containing the center of gravity of the 
system. This layer, called the immovable layer, is practi- 
cally taken at the bottom of the bore, where experiment 
shows that the maximum pressures occur. See page 17. 



VII. — PRESSURE GAUGES. 



General Methods Adopted. 

Two general methods for measuring the intensity of the 
pressure are employed, viz.: 

1. Statical. 

The statical, in which the elastic pressure is placed in 
equilibrio with a known resistance. The objections to this 
method relate to the magnitude of the forces to be measured 
and to the rapidity with which they vary. It is principally 
valuable for determining the intensity of the maximum 
pressure at the point at which the measurement is made. 

2. Kinetic. 

In which the intensity of the pressure at any instant is 
deduced from the acceleration given to a known mass. 

The objections to this method relate to the minuteness of 

the times to be measured and to the consequences of small 

. . . A''^ 
errors m measurmg the spaces, smce a= 

By the use of comparatively simple apparatus it permits 
the law of the variation in pressure to be approximately 
determined. 

I.-THE STATIC METHOD. 
Rumford's Plan. 

In 1792, Count Rumford, who made the first recorded 
experiments on powder pressures, sought to measure the 
total pressure, P=/ 7t r% of a charge of gunpowder fired in 
the closed bore of the eprouvefte, Fig. 1, by determining 
the greatest weight, W, that would be lifted by the gas suffi- 
ciently to allow the escape of gas to cause an audible report. 
Conversely, the weight and the volume being constant, he varied 

W 
the charge. In either case he assumed P— W oi fiz=. r 

But if we represent by /, the time during which the gases 
were lifting the tenon of the stopper through the height h^ 



VII. — PRESSURE GAUGES. 



the general expression Mgl = M = P- JV, (whence 



/i = 



F^W 



df 



t \ '^^ 

yf^ ^ J shows that, / being very small, P must have 

greatly exceeded W in order that h should have had an 
appreciable value. 
Process of Deformation. 

This, which is the present method, consists — 

1st. In determining with a press the tarage^ or law con- 
necting known pressures with the observed permanent de- 
formations of similar metallic specimens. 

2nd. Exposing a similar specimen to the action of powder 
gases acting over a known area; observing the resulting 
deformation, and inferring from the tarage the intensity of 
the total pressure producing the deformation observed. 
Methods of Deformation. 

The specimen may be deformed in several ways — 

1. By making a cut, the length of which increases more 
rapidly than its width. Fig. 2. 

This is General Rodman's plan. 

2. By compressing a cylinder between flat surfaces. 
This is Captain Noble's crusher gauge, now generally 

employed. 

Both methods are adapted for service either within or 
without the bore. 

Apparatus, 
Specimens. 

On account of its homogeneity, copper is generally used for 
the specimen, although lead, and even silver, are employed. 
Pistwi. 

The pressures are exerted through a freely moving piston. 
When firing, a gas check of some kind prevents the gas from 
leaking past the piston. 
Gas Checks. — 1. Cup. 

The action of this gas check, which illustrates a principle 
of frequent application in ordnance, depends upon the 
excess of the pressure within the cup over that without it; 



VII. — PRESSURE GAUGES. 



since any gas that may leak past the edge before it is 
fully dilated will expand so readily as to have its density 
greatly reduced in comparison with that of the gas within 
the cup. 

2. Air Packing, 

Another form of gas check depends upon a number of 
circumferential grooves, surrounding the stem of a closely 
fitting piston, Fig. 4. These diminish successively the 
tension of any intruding gas and delay its progress, until, 
by the departure of the projectile from the gun, the pres- 
sure ceases. This principle also is applied in ordnance 
construction. 
External Housing. 

For external use the gauge is contained in a housings 
screwed into the walls of the gun and communicating by a 
radial hole with the bore. This method is rarely employed 
at present. ^ 

Internal Housing. 

For internal service a housing, Fig. 3, contains all the 
parts. The drawing represents a Noble internal crusher 
gauge, full size. 

A is the specimen; B, the cavity; C the body of the 
housing, closed by the screw y and the soft metallic gasket K. 

I is the piston, the cross section of which is y^^ of a 
square inch in area. It is enlarged at E to accommodate 
itself to the dilatation of A. 

Z> is a cup-shaped copper gas-check acting like a metal- 
lic cartridge case, and F is a spring to keep the specimen 
in an axial position. 

Use of Internal Gauge. 

To use the gauge, it is tied to the bottom of the cartridge 
so that no powder can pass between it and the bottom of 
the bore. 



VII. — PRESSURE GAUGES. 



It is sometimes recessed into the face of the block of 
breech loading guns, so that full charges may be fired. It 
has also been similarly recessed into the base of the pro- 
jectile. 
Advantages of Crusher over Rodman Gauge. 

The advantages of the Crusher over the Rodman gauge 
are: 

1. Size. 

The small diameter of the specimen, which enables the 
size of the housing to be greatly reduced. 

When used internally, the circumstances are therefore 
more nearly normal, and, when used externally as in Fig. 13, it 
maybe inserted close to the walls of the bore instead of ex- 
ternally to the gun as with Rodman's first gauge. Fig. 2. 

In the latter case it was found that the gas developed con- 
siderable kinetic energy in its passage through the walls 
of the gun and struck the pi.ston a blow which vitiated the 
results of the experiment. This action accounts for many 
anomalies in the early experiments. 

When properly used, the fact that the gases act by a 
pressure and not by a blow is shown by the sensible persist- 
ence of form of a specimen exposed to several similar dis- 
charges, and by the experimental verification of calculations 
based upon this statical hypothesis. 

2. Surface. 

The flat face of the piston is less liable to injury and 
admits of duplication more easily than does the Rodman 
knife. 

3. Tarage. 

It also admits of giving to the specimen a preliminary 
compression before it is exposed to the action of the gas. 

This, if nearly equal to that expected within the gun, 
diminishes the velocity which the piston can acquire (see 
^ost) ; it also serves to verify the tarage. 



VII. — PRESSURE GAUGES. 



EFFECT OF VARYING THE MASS OF THE PISTON. 

Discussion. % 

Let /* be the variable gaseous pressure on the piston ; R the 
variable resistance to deformation of the specimen; m the 
mass of the piston, and v its variable velocity over the 
path X. 

Let d represent the permanent compression. 

Suppose the piston to be in contact with the specimen 
and to be indeformable. 

We have: 

' ^/lPdx-/lRdx. (1) 



2 

When X is a maximum, v—o\ x^^d, and the equation (1) 
becomes 

/\pdx=f\Rdx. (2) 

Let the curves AFE and BFC in Fig. 5 represent by 
their ordinates, respectively, the resistances and pressures 
due to successive values of x, and let x represent only 
permanent deformation, /. <?., that occurring beyond the 
elastic limit of the specimen. 

From the nature of powder pressures as hereafter ex- 
plained, Chap. XI, the pressure curve will be of the general 
form OABC\ and, if OD—d, we have area 

OABCDrz^f'^^Pdx, 

From the nature of the resistances to deformation, the 
curve AFE will present no maximum phase, and the curve 
will be of the general form AFE, such that the area 

OAEn=^ f^'Rdx. 



■/> 



Equations 1 and 2 show that the resistance curve, at first 
beneath the pressure curve, rises above it when x has some 
value = OH, 



Vn. — PRESSURE GAUGES. 



The statical value of the ordinate E,D^ corresponding to the 
maximum compression OD, is determined from the tarage. 

The figure shows that, while ED may be greater or less 
than IB^ which represents the maximum gaseous pressure, 
the difference between these two ordinates will depend 
upon the angle at which the curves intersect. If this angle 
be such that the difference, P — R, of any two ordinates 
corresponding to a common abscissa be relatively small, the 
resistance corresponding to the maximum compression may 
safely be taken as the maximum gaseous pressure. 

But P-R= ^ ^ ,= ma (3) 

doc 

So that the difference between ED and IB can be 
neglected only when the mass of the piston is small and the 
initial resistance to deformation is great and increases rapidly. 

The last two conditions are satisfied by a preliminary 
deformation of the specimen to nearly the total extent that 
is expected. Such conditions are represented by figure 6. 

The indications of the gauge will be more correct when 
the pressure curve approaches parallelism with the axis of 
X. It will be seen that this occurs rather with slow-burn- 
ing powders, which give a gradual change of pressure, than 
with those which act more violently. 

Tarage. 

The preceding discussion shows that the pressures used 
in determining the tarage must be applied so slowly that the 
velocity of the piston and of the contiguous parts of the 
machine may be neglected. Under such circumstances, 
when the specimen is of pure copper, 8 mm. in diameter 
and 13 mm. long, the resistance in kilogrammes, T, corres- 
ponding to a permanent compression in millimetres, E^ is 
given by the following equation. 



VII. — PRESSURE GAUGES. 



^=551 +531 E, 
The tarage would accordingly be represented by a dia- 
gram, such as Fig. 7, the initial ordinate being at the elastic 
limit, and the co-efficient 531=tan ^, or the reciprocal of 
the rate of permanent compression. 

V SARRAU'S DEDUCTIONS. 

An elaborate deduction by M. Sarrau, shows by an 
analysis confirmed by experiment that,^- 
Slow Pressure. 

I. When the pressure increases slowly, as when the 
crusher is used in the chamber of a gun firing ordinary 
gunpowder, the maximum pressure is sensibly equal to that 
indicated by the tarage. 

ftuick Pressure. 

II. When the pressure is instantaneously, or very sud- 
denly applied, as with some of the high explosives; or 
when, with ordinary gunpowder, the crusher is placed in 
front of the position occupied by the projectile when at 
rest so that the pressure shall be very suddenly applied 
when the base of the projectile has passed the mouth of the 
hole; then the maximum pressure is sensibly equal to that 
corresponding to half the tarage. 

The correction increases with the mass of the piston 
employed. 

THE MANOMETRIC BALANCE. 

Object. 

This avoids the perturbations due to the mass of the 
piston, and permits certain relations between pressures and 
time to be determined. 
Simple Form. 

B, figure 8, is a differential piston, the small end of which 
is in contact with the bore, and the large base of which enters 
slightly the air-tight cavity C, connected with a manometer 



VII. — PRESSURE GAUGES. 



tube, M, in which mercury is kept at any given height by 
means of air pumped into C. 

A slide, a, is held by friction beneath B against the ten- 
sion of a spring, r. 

The pressure may be determined within limits by finding 
at two successive similar fires, the heights of the mercury 
permitting and preventing the motion of a. 

Compound Form. 

Also by providing, say, ten similar pistons of varying 
area, moving outwardly from Cj each of them provided, 
besides the arrangement ra, with some apparatus such as 
described Chap. VI, for recording the intervals of time 
corresponding to the motion of the slide a. 

II. THE KINETIC METHOD. 

This consists in determining the rate of change of the 
pressure from the change in rate of motion of some body, 
the mass of which is known. This body may be either 
I, the projectile; II, the cannon; or III, a piston or auxiliary 
projectile, placed in some radial channel communicating 
with the bore. 

I. THE PROJECTILE. 

1. Direct Intermittent Method, 

Mayewski's Experiments. Figure 16. 

General Mayewski, of Russia, in 1867, attempted to 
determine the acceleration of the projectile by attaching to 
its base a rod which, passing through the breech of the 
gun, ruptured by means of a projection upon it certain 
electric currents placed at varying distances from the 
initial position of this projection. The conditions of each 
fire were made constant, except as to the portion of the 
path of the projectile, the duration of which was to be 
measured. 



10 VII. — PRESSURE GAUGES. 

Supposing that x~f[t), he assumed a development 

x=At+Bt^-{-Ct^ + nt'' + Qtc., (4) 

and determined by trial the values for the co-efficients, A, B^ 
etc., that would satisfy the instrumental values x and /. 
Then, 

dx 
dt 



=A^%Bt-{-ZCt^ + ^nt^^-tio. (5) 



d^x 
a=-^=2B + %Ct+12nt^ + ttc, (6) 

The value of t corresponding to the manimum pressure 

d^x 
wasfoundby placing— 3 =0, and solving with respect to /; 

then, by substitution in equations (1) and (3), the corres- 
ponding values of x and a were found. 

The intensity per unit of area of the corresponding pres- 
sure, is given by the following equation: 

d'^x 

This pressure is only that giving acceleration to the 
projectile. The results, found by adding to B=p n r^ the 
pressure found to be required to force the projectile 
through the bore, gave reasonably close approximations to 
the results of the statical pressure gauges, altiiough the 
apparatus was subject to many instrumental errors. 



2. Direct Continuous Method, 
Sebert's Registering Projectile. 

This method, which is applicable only to comparatively 
short lengths of bore in guns of large caliber, requires a 
hollow cylindrical projectile, such as is shown in Fig. 9. It 



VII. — PRESSURE GAUGES. 11 

is provided with an axial spindle, S, of rectangular cross 
section and rotating freely at each end; one of the sides of 
this spindle is covered with a film of soot. 

A slide M moves freely on the spindle and bears a 
delicate tuning fork 7^ arranged as described, Chap. VI. 

When the projectile is fired, the inertia of the slide holds 
it relatively at rest while the projectile passes by; the 
points of the tines describe such a trace as is shown in 
figure 10, in which the parallel straight lines represent the 
traces when the slide is slipped along the spindle, the fork 
not vibrating. 

The effect of the friction between the slide and the 
spindle can be shown to be negligible. 

Although the path of the slide is limited to less than the 
length of the projectile, yet it is within this length of travel 
that is generally found the maximum pressure, the rate of 
change in reaching which is one of the most important 
objects of research. 

By placing the slide at the bottom of the spindle, it may 
serve to determine the retardation of the projectile in flight; 
and, by confining it there by a fragile cross-pin to be broken 
on impact, it may determine the varying resistance found in 
penetrating a more resisting medium than the air. 

3. hidirect Intermittent Method. 
Successive Shortening of the Bore. 

The mean of the muzzle velocities of a large number of 
shots fired under conditions, which, excepting the length of the 
bore, were identical, could be laid off as the ordinates of a 
curve of which the abscissae should represent the various 
paths. The curve would have the form given by Fig. 11. 
Calling a the acceleration, we have, 

dv dv dx dv /i\ 

dt dx dt dx 



12 VII. — PRESSURE GAUGES. 



The figure shows that the subnormal a= corresponding 

ordinate v x tan g? = ?; x -r- • (") 

^ ax 

Therefore, having plotted the curve expressing 
v=f(x), 
the acceleration at the different points along the bore may 
be determined by finding the corresponding values of the 
subnormals. 

The experiments enabled positive conclusions to be 
formed : 

1st. As to the smallness of the advantage gained by in- 
creasing the length of the bore more than 20 calibers, when 
quick powders were used. 

2nd. As to the great advantage of progressive powders in 
guns of suitable length. 

II. THE GUN. 

Advantages. 

Determining the pressure from the acceleration of the gun 
in its recoil affords certain advantages owing: — 

1st, To the low velocity of the gun compared to that of 
the projectile; this permits a greater number of observations 
to be made over a given path. 

2d. To the simplicity of the apparatus, which avoids the 
mutilation of the piece, and permits it to be used with guns 
of varying calibers. 

3d. To the aid given in the study of the pressures pre- 
vailing at the bottom of the bore. 

1. Rodman's Velocimeter , 
Construction. 

The original instrument of this description was devised 
by General Rodman. It consisted of a cylinder rotating 
with a known and uniform velocity about an axis parallel 



Vll. — PRESSURE GAUGES. 13 

to that of the gun and close to it, A pointer fastened to 
the gun traced upon the cylinder during the recoil, a line 
which, when developed, gave the successive accelerations of 
the recoil. The gun was hung as a pendulum oscillating 
in the plane of fire. See figure 17. 

Acceleration of Eecoil. 

For example, let mm' ^ Fig. 12, be the developed circumfer- 
ence traced by the pointer when the projectile is placed at the 
muzzle, and the charge uniformly dispersed along the bore ; 
and let bb' be the corresponding circumference when the charge 
is in place. Then taking axes of space and time, ^S" and T 

a = 7 — -ri, as in Chap. VI. 

Tlniform Pressure. 

The dotted line represents the parabola which would be 
traced under the ideal circumstances discussed, Chap. V, 
/ V being straight and parallel to t' v' . 

Rate of Change of Pressure. 

It is evident, from the inclination of the initial portions 
of the curve, that ihe velocity is actually acquired much more 
rapidly than is desired. 

2. Siberfs Velocimeter, 

Construction. 

The velocimeter of Colonel Sebert of the French service 
replaces the rotary cylinder by a broad steel tape, one side 
of which is smoked, and against which rest the tines of a 
tuning fork set vibrating by the act of recoil. See Chap. 
VI. 

Velocity of Recoil. 

The length of any double vibration measured on the 
tape, divided by the time of the double vibration of the 



14 Vll.— PRESSURE GAUGES. 

fork, gives us the mean velocity of recoil over that portion 
of the path selected; from which, calling, 

qv =z weight of projectile. 

JV = weight of gun. 

«/ = weight of powder. 

2j = velocity of projectile. 

V = velocity of gun. 

We have V= -^ (see Chapter VI). 

Velocity of Projectile. 

Or else, supposing the center of mass of the powder to be 
moved to the position occupied by the center of mass of the 
gases, which is equivalent to supposing that half the mass of 
the powder is added to that of the projectile. 

-= --^r (9) 

Position of Projectile. 

Also, denoting by X the length of recoil at the end of a 
time t, and x the corresponding path of the projectile. 

Pressure on Base of Projectile. 

The method above described permits the construction of 
a velocity curve, such as Fig. 11, from which the pressure 
corresponding to different positions of the projectile along 
the bore may be deduced. 
Pressure on Base of Bore. 

Also, the difference between two successive velocities, as 
determined by the trace of the tuning fork, divided by the 
common interval of time, would give the mean accelera- 
tion ; this multiplied by the mass of the gun gives the mean 



Vn, — PRESSURE GAUGES. 15 



total pressure on the bottom of the bore during the same 
interval of time. 

III. AUXILIARY PROJECTILES EXPELLED THROUGH THE 
WALLS OF THE GUN. 

1. Bomford's Method. 

About 1841, Colonel Bomford, of the Ordnance Depart- 
ment, prepared a cannon by boring through its walls a 
series of small holes at right angles to its axis, as in Fig. 13, 
and placing in each hole a bullet, the velocity of which was 
instrumentally determined. The pressure at the various 
points, deduced from the velocities communicated to the 
balls, determined the form of the old Columbiads. 

This method was objectionable, as it treated the powder 
pressure as an impulsive force and could not take into 
account the varying accelerations of the projectile, as is 
done in the following recent inventions. 

2. Ricqs Register^ Fig. 14 

A cylinder C, revolving with known and uniform velocity, 
is enclosed in a box B^ through a groove, Z>, in which slides a 
marker F^ in contact with the piston Z. 

The weight per unit of the sectional area, ^, of (F-Vl^ 
may be varied at pleasure. 

When the gun is fired, a curve, such as shown, is traced 
on the cylindery from which, by finite differences, we have 

^= -,. (11) 

^= ^(KJf (12) 

8. T/ie French Accelerograph, 

This projects vertically upward a piston, the mass of 
which may be greatly varied by the addition of weights. 



16 



VIT. — PRESSURE GAUGES. 



A fixed tuning fork traces the harmonic curve upon a 
blackened surface on the piston. 

III. STATIC AND KINETIC METHODS COMBINED, 
Objections to Kinetic Method. 

It will be seen that the objection to the kinetic method 
lies in the liability of error in the measurement of the small 
spaces by which the time record is expressed. 

This limits the method principally to the cases where the 
pressure changes but slowly, as in those powders known as 
slow-burning powders. 

Noble's Experiments. 

In 1869, Capt. Noble, R. A., prepared a M. L. gun as 
.described, Chap. VI. Crusher gauges were placed in the 
holes leading to the chamber, and the other holes were 
provided with the apparatus also given in Chap. VI. 

By observation and interpolation, a table of spaces and 
times was formed so as to make A x constant=6, 10°^, as 
follows: 









7J ^^ 






Av 


/- ^ a 


X 


/ 


At 


At 


A V 


logdt 


dt 


^ Ttr^g 


mm. 


sec. 


sec. 


m. s. 


m. s. 


* 


m. s. 


kil. per 
c=] cm. 


0.00 
6.10 


0.0000000 
0.0018182 


0.0018182 


8.85 














0.0005590 




7.56 


4.88327 


9891 


271 


12.20 


0.0023772 




10.91 














0.0002528 




9.02 


4.61517 


22082 


005 


18.30 


0.0026330 




19.33 











* The values of dt are obtained by interpolation. That of the mean 



acceleration for the first value of Az^, viz., A/= 



0.0023772 



=0.0011886 



would evidently be too large, and the corresponding value for /=186.5 
would be too small. The method of interpolation is similar to that here- 
after described in Exterior Ballistics. 



VII. — l-KESSTTRE GAUGES. 17 

Fig. 15, represents the curves obtained in a 10 in. gun 
firing a 300 lbs. projectile with fine (R. L. G.), and coarse, 
(Pebble) powders. 

The muzzle velocity of the projectile was in both cases 
practically equal. 

Comparison of Results. 

The calculated pressures agreed closely with those ob- 
served in the gauges placed near the base of the projectile 
when at rest; and those observed at the base of the bore 
considerably exceeded those observed near the base of the 
projectile. ^^^. Chap. XI. 



VIII. — PHENOMENA OF CONVERSION. 



CHAPTER VIIL 

PHENOMENA OF CONVERSION. 

Phenomena. 

For purposes of analysis the conversion of gunpowder 
into gas may be considered under tliree heads, viz.: Ignition^ 
Inflammation and Combustion, 
Definitions. 

By Ignition is meant the setting on fire of a particular 
point of a grain or charge. 

By Inflamination is meant the spreading of the fire from 
point to point of the surface of a grain, or from one granu- 
lar surface to another throughout the charge. 

By Combustion is meant the passage of the inflamed 
surface throughout the substance of each grain. 

IGNITION. 

Gunpowder is the most refractory of the explosives; it 
ordinarily requires a temperature of 300°. Its ignitibility 
varies inversely: 

1st. With the amount of moisture present. 

2d. With the smoothness and sphericity of the surface. 

3d. With its density. 

It also varies with the character of the charcoal. 

COMBUSTION. 
Definition. 

By velocity of combustion is meant the rate of motion of 

the inflamed surface in a direction normal to that surface. 

Owing to the impossibility of determining this within the 



VIII. — PHENOMENA OF CONVERSION. 



gun, the velocity of combustion of different kinds of 
powder in the open air is taken by the manufacturer as a 
rude means of comparing their combustibility. 
Determination. 

If the size of the grain permits the time of its burning to 
be accurately determined, this simple method is preferred; 
since it resembles most closely the actual conditions of prac- 
tice. Otherwise, we may extend the time to be measured 
by burning, like a candle, a prism of press cake having its 
sides greased to protect them from the flame; or else, we 
may use a tube rammed with the pulverized mill cake of 
the same density as that of the powder to be tested. So 
determined, the velocity is found to be about 0.4 inch per 
second. 
Nature of Combustion. 1. In Air. 

This experiment proves that the composition burns in 
parallel layers at a uniform rate; so that the combustion of 
a spherical grain would resemble the peeling of an onion. 

This fact is frequently illustrated on the proving ground, 
where burning grains of powder are projected from the gun 
with sufficient force to penetrate deeply into wooden 
boards. Should they fall in snow, their appearance will 
plainly indicate the superficial nature ot their combustion. 
2. In Gun. 

It is important to remember that the velocity of combus- 
tion within the gun is very much greater and less uniform 
than that in the open air. The process resembles roughly 
the absorption of water by a porous substance when under 
variable hydrostatic pressure. The effect may be, not only 
to accelerate the velocity of combustion, but also, by break- 
ing up the grains, to increase the burning surface; as we 
crush sugar to facilitate its solution. 

The velocity of combustion is supposed to vary directly 
with the intensity of the gaseous pressure. 



VIII. — PHEKOMENA OF CONVERSION. 



CIRCUMSTANCES AFFECTING THE VELOCITY OF COMBUSTION 

IN AIR. 

Varying Conditions. 

Under similar circumstances the velocity of combustion 
of homogeneous powder is constant. It varies however, 
with the purity^ proportions^ incorporation^ density and con- 
dition of the powder as follows; 

1. Purity. 

The nitre and sulphur should be pure, or nearly so. The 
part that charcoal plays depends upon its combustibility. 
This is determined by finding the velocity of its combus- 
tion, when incorporated with a due proportion of nitre in 
such a tube as above described. 

2. Proportions. 

By varying the proportions, all velocities up to 0.55 inch 
per second can be obtained. 

The proportions usually adopted are those that give the 
greatest volume of gas in a given time, because the mass 
burned is the greatest, and because each unit of mass gives 
the greatest volume of gas. 

3. Incorporation. 

Prolonging the incorporation increases the velocity at a 
rate which increases as the proportions approach those 
adopted. 

4. Density. 

With each set of proportions a density is soon reached 
that corresponds to the maximum velocity. Beyond this 
density the velocity varies inversely as the density, at a rate 
which increases as the proportions approach those adopted. 

The increase in superficial density due to glazing dimin- 
ishes the velocity of combustion; provided that the dust 
formed in the process be removed. 



VlII. — PHENOMENA OF CONVERSION. 



5. Condition. 

The velocity increases with the porosity of the powder. 
See page 2. The porosity may result from the evaporation 
of water, alcohol, or vinegar, added to the substance before 
pressing it. When porosity is carried to the point of fria- 
bility, the consequences described, page 2, may be expected. 

AVhen oils, gums, or resins are added, or when an excess 
of water remains in the composition, the velocity of com- 
bustion is diminished. An excess of water permits the nitre 
to segregate and to neutralize the effects of incorporation. 

Re7nark< 

These variations should be carefully studied, as upon 
them depend the most important characteristics of gun- 
powder. 
Emergency Powder. 

For example; during the Franco-German War of 1870, it 
was found necessary to increase, far above their normal 
capacity, the product of the powder mills remaining in the 
hands of the French. 

This was accomplished by reducing the time of incor- 
poration under the wheels, besides calling into use the stamp 
mills and rolling barrels formerly employed for this pur- 
pose. 

The effect of less thorough incorporation upon the 
velocity of combustion was neutralized by reducing the 
density of the powder. 

This answered well where the powder was not intended 
to be stored, and where the capacity of the chambers in 
which it was to be fired permitted a corresponding increase 
in the volume of the charge. 

The differences of the effects upon the gun and its pro- 
jectile, resulting from varying the phenomena of combus- 
tion, are described in Chapters X and XI. 



VIII, — PHENOMENA OF CONVERSION. 



INFLAMMATION. 
Hypothesis. 

The inflammation of a single grain is generally assumed 
to be instantaneous, and so is that of a charge of powder; 
unless the time of its inflammation bears so considerable a 
ratio to that of its combustion that the total time required 
for the conversion of the charge into gas is sensibly in- 
creased. 

Experiment. 

The nature of the process may be studied by determining 
the time required to inflame trains of powder of known 
lengths under various conditions. 

Varying Conditions. 

The velocity of inflammation is found to vary: 

1. With the disposition of surrounding bodies. 

2. With the size and shape of the grains. 

3. With their composition and constitution. 

1. Confinement. 

The heated gases, evolved by ignition, follow in their ex- 
pansion the line of least resistance. If they are confined, 
so that this line coincides with that along which the powder 
is disposed, its rate of inflammation is increased. Thus, the 
velocity of inflammation of a train is increased by firing it 
in a tube instead of in the open air. It is still further 
increased when the cross-section of the tube is not entirely 
filled; and when the bottom of the tube, near which the 
train is ignited, is closed, as in a gun. 

2. Size and Shape of Grain. 

The size and shape of the grain affect both the force 
propelling the gases and the resistances which they encoun- 
ter. In the first case, the size and shape of the grain affect 
the amount of gas evolved in equal successive times and 
also the ignitibility of the unburned grain; in the second 



VIII. — PHENOMENA OF CONVERSION. 



case, they affect the size and shape of the spaces between 
the grains. So that, in fine powder, although the gaseous 
pressure may be greater, the resistance to the passage of the 
wave of inflammation may also be greater. In coarse pow- 
der the converse may be the case. The velocity of inflam- 
mation should therefore be determined by experiment. 

It is now much less important than when muzzle loading 
guns were in use. 

If the charge be made of mealed powder compressed, 
there will be no interstices; and the velocity of inflammation 
and that of combustion will be the same. 

If it be of concrete powder, the velocity of combustion of 
the entire grain will be that of the inflammation of the con- 
stituent grains, and will be greater than that of the com- 
pressed mealed powder above referred to. 

This ratio was found to be as 1.4 to 1.0. 
3. Composition and Constitution. 

The velocity of inflammation is affected by variations 
in the purity and proportions of the ingredients, in the 
thoroughness of their incorporation, and in the density of 
the powder, in so far as these affect its velocity of combus- 
tion and its susceptibility to ignition. 



IX. — NOBLE AND ABEL's EXPERIMENTS. 



CHAPTER IX. 

NOBLE AND ABEL'S EXPERIMENTS. 

From 1868 to 1874, Captain Noble, R. A., and Mr. F. Abel, 
the chemist of the British War Department, made a series 
cf experiments upon gunpowder that have become his- 
torical. 

NATURE OF THE EXPERIMENTS. 

These experiments were conducted on the principle, 
general in all experimental comparisons, of keepmg all con- 
ditions constant except that of the variable under consideration. 

Although their ultimate object was to determine the 
behavior of fired gunpowder in the variable volume behind 
the projectile in a gun, this principle required that their 
preliminary experiments should be conducted in closed 
vessels, the capacity of which was invariable and accurately 
known. 

VARIABLES. 

They accordingly varied: — 

1. The composition of the powder. 

2. The size of its grain. 

3. The mass of gunpowder exploded in a given volume, 
or the density of loading. 

FUNCTIONS. 

Under these different circumstances they observed: — 

1. The maximum pressures per unit of area. 

2. The composition and condition of the products of 
combustion. 



2 IX. — NOBLE AND ABEL's EXPERIMENTS. 

3. The specific volume of the gases formed, viz^ at a 
pressure of one atmosphere and at 0°. 

4. The quantity of heat evolved by the combustion. 

CONCLUSIONS. 

From the observed states of the functions corresponding 
to particular values of each variable they sought to 
determine the law expressing the relation between pres- 
sures, volumes and temperatures in closed vessels, with the 
view of applying it to the variable conditions existing in 
guns. 

METHODS FOLLOWED IN THE EXPERIMENTS. 

VARIABLES. 

1. Composition of Powders. 

Four of the six kinds of powders tried were approxi- 
mately of the usual composition. The others differed 
notably as seen by the following table: 

COMPONENTS. POWDERS. 

Four English. Spanish. Blasting, 

Nitre, 74 

Carbon, 12 

Sulphur, 10 

Water, H, O, Ash, etc., 4 

100 100 100 

2. Size of Grain. 

The principal experiments in which the size of grain 
entered as a variable were those in which comparisons 
were made between R. L. G. (Rifle, large grain) and the 
Pebble powders referred to Chap. VII. The linear dimen- 
sions of these powders were about as 1 to 3. 

3. Density. 

It is evident that the results of the experiments were 
largely dependent upon the relation existing between the 



75 


62 


9 


18 


12 


15 


4 


5 



!X. — NOBLE AND ABEL's EXPERIMENTS. 



mass of the charges and the volumes in which they were 
fired. This requires a discussion of the density of powder 
which is named under three heads. 

1. Specific Gravity. 

By density simply, or d, we mean the specific gravity of 
the press-cake, or that of the individual grains, referred to 
water. This in practice ranges from 1.68 to 1.85. The 
maximum attainable density calculated from that of the 
ingredients of gunpowder united in their ordinary propor- 
tions, is 1.95. 

2. Gravimetric Density. 

By this term, or y^ we mean the density referred to water 
of grained powder, including its interstitial volumes; or, 
calling w, the weight in pounds of one cubic foot of the 
loose powder. 

^~ 62.425 ^^ 

The gravimetric density is sometimes expressed by the 
weight in ounces of one cubic foot of the loose powder. 

The gravimetric density of powder is important when it 
is to be used in a limited 'volume as in the cartridges for 
breech-loading small arms and in explosive projectiles. It 
is evident that the form of grain and the amount of settling 
affect the interstitial volumes and hence its value. For 
loosely piled powder of irregular granulation it is about 0.9. 

Specific and Interstitial Volumes. 

The amount of the interstitial volumes, which, as seen in 
Chap. VIII, affects the rate of inflammation, may be de- 
termined as follows: 

Let F, represent the volume of the powder when loose; 
v,^ its specific volume, or its volume when compressed to a 
uniform density, 6 ; and v' ^ the sum of the interstitial volumes : 
then, since w = F y = z^, (5. 



IX. — NOBLE AND ABEL S EXPERIMENTS. 



d : y :: V W or v=y -k- (2) 

whence v'= F-v= F ^^"^^ (3) 

Ordinarily, d is about 1.8; and, when the powder is loosely 

y 
piled, V is about 0.9. In such a case v=v^= -^. 

Noble conducted his experiments with powder so closely 
packed that y was sometimes equal to unity: in such a case 
v' was sensibly equal to 0.44 F. 

3. Density of Loading. 

By this term, or A , we express the relation between the 
mass of a charge of powder and the volume in which it is 
fired. 

If the values of S and y were constant, it would suffice to 
say that the cavity holding the powder was, say, one-half, 
three-quarters full, etc. This was the method adopted by 
the early experimenters. 

But the quantity of matter in a given volume of grained 
powder may vary from both the causes named. 

The value of A is therefore taken as the ratio of the 
weight of the powder fired, to the weight of water at its 
maximum density which would fill the volume in which the 
powder is fired. Calling this volume expressed in cubic 
feet F, and expressing w^ as before, in pounds, we have 

w 
^ ^ Fx 62.425 (^^ 

It is usual to give the linear dimensions of guns in 
mches; therefore calling z;= Fx 1728, the volume in cubic 
inches, we have 

• ,^^^ (5) 

This value of A is of constant application and must be 
remembered. 



IX. — NOBLE AND ABEL's EXPERIMENTS. 



APPARATUS. 

The vessels employed were strong steel cylinders as 
shown in Fig. 1. Each one contained a firing plug, F^ with 
a conical stopper, /, insulated from 7^ by a washer, w, and by 
sheet of tissue paper wrapped around its body. Another 
conical screw plug, P, carried a crusher gauge, C. 

The object of the form given to F and P was to facilitate 
their removal; since a very slight motion would free them 
from the walls. 

The charge was ignited by an electric igniter, /. 

After the firing the vessel was immediately conveyed to a 
calorimeter; or a smaller vessel. Fig. 2, could be fired 
under water. 

FUNCTIONS. 

1. Pressures. 

These were determined by the crusher gauge, and the 
observed results compared and corrected by the methods 
used in experimental research. 

2. Nature of Products. 

Small samples of gas were drawn off for analysis through 
the tube, E, opened by slightly unscrewing the valve e. 

The initial liquidity of the non-gaseous products was 
determined by tipping the cylinder in various directions 
soon after the explosion, and by observing the appearance 
of the solid crust when the vessel was finally opened. 

3. Volume of Gases. 

The specific volume of the gases was determined by a 
gasometer. Fig. 3. The long wTench, w, passing through 
the stufhng-box, sb^ was used to unscrew P^ immediately 
after the explosion. 

4. Heat. 

The quantity of heat evolved by the conversion was 
determined by immersing the vessel in a calorimeter con- 



6 IX. — NOBLE AND ABEL'S EXPERIMENTS. 

taining a known weight of water of known temperature, 
and by noting the resulting rise in temperature. 

RESULTS OF THE EXPERIMENTS. 

STATES OF THE FUNCTIONS. 

1. Pressures. 

For all kinds and sizes of powder the pressure was found 
to be practically constant for equal densities of loading, or 
the force o( SiW the powders was the same. When A=l, 
the force was about 6,400 atmospheres, or 43 tons, or 
96,000 lbs., per square inch. 

2. Products. 

The following table* gives, by weight per cent, the mean 
proportions of the products resulting from many experiments; 

PRODUCTS. KINDS OF POWDER. 

Gaseous. Tour English. Spanish. Blasting. 

CO2, 

CO, 

N, 
Various, 

Total Gaseous, 

Non-Gaseous. 

K, CO3, 
K2SO4, 
Ka S, 
Various, 

Total Non-Gaseous, 66 62 49 

From the appearance of the cavity after firing, the non- 
gaseous products were supposed to be suspended at the 
instant of the explosion as a highly heated liquid spray 
which eventually assumed a solid form. In cooling it was 



26 


25 


23 


3 


1 


15 


11 


11 


9 


4 


1 


4 


44 


38 


51 


34 


22 


19 


12 


30 




6 


6 


17 


4 


5 


13 



*NoTE. — The relative proportions of the total gaseous products and of 
CO, should be learned. See Chapter II, 



IX.- 



supposed to shrink from about 0.6 the volume of the entire 
charge, or 0.6 F, page 3, to about 0.3 V. 

Confining our attention to the typical English powders it 
is significant to observe that very nearly the same propor- 
tions were concluded to exist between the volumes occu- 
pied by the gaseous and non-gaseous products at the instant 
of the explosion, as were found to exist between the weights 
of these products and between the interstitial and specific 
volumes of the charge. 

That the non-gaseous products did not, by their volati- 
lization, augment the volume of the gases was inferred from 
their behavior when exposed, solid, in a Siemen's furnace, 
to a temperature of about 1700°. At this temperature 
which, although the highest available, was about 700° lower 
than that determined by calculation, the solids swelled to 
nearly twice their volume, but did not volatilize. 

3. Volumes. 4. Heat. ^ 

The relations between the specific volumes of the gases 
and the calorific values of the powders appear from the 
following table which illustrates the curious fact, noted in 
Chap. II, that their product is approximately a constant 
quantity. The volumes are referred to that occupied by tlie 
powder when A = 1. See note 1, page 13. 

Kind of Powder. Specific Volumes. Heat Units Products, 

or vq. or H. 

English powders, 264 737 194568 

Spanish powder,, 234 767 179478 

Blasting powder, 360 517 186120 

Had the experimenters known the specific heat of the 

products of combustion when at a constant volume, or C^, 

the absolute temperature of the conversion, or Tq, might 

have been determined from the general equation, 

If 



IX. — NOBLE ANt) ABEL*S EXPERIMENTS. 



but, although the same products were always formed, they 
occurred in such varying proportions, even when all the 
conditions were as nearly as possible identical, that no 
certain conclusions could be made. Chap. II, page 7. 

Also, by taking the mean specific heats of the mean of 
the non-gaseous products, when in a solid form, and also of 
the gases, a temperature was computed which was mani- 
festly too great. The experimenters accordingly adopted 
the following course in which the deductions of theory are 
corrected by experiment. 

Temperature of Explosion. 

Assuming the general equation for the work of perma- 
nent gases subjected to changes in temperature, or — 

pv=^rt, (6) 

in which r is a constant, and t is reckoned from absolute 
zero; let us express/ in atmospheres. 

The preceding table gives for the English powders a 
mean value of r= (264 = v) (1 =/) v (273 = /) = 0.967. 

Substituting the values of v and / for A zz: 1, we have — 
/= (6400) (0.4) ^ 0.967 = 2646° absolute, = 2373° C 

This was verified for varying values of A and by the ex- 
posure to the temperature of the explosion of very fine 
platinum wire which melts at about the temperature above 
determined. 

CONCLUSIONS. 
Fundamental Hypothesis. 

The remarkable compensation between the volumes of 
gas generated and heat evolved permitted Noble and Abel 
to apply to these gases the laws of Mariotteand Gay-Lussac; 
provided, that from the volume of the chamber in which the 
explosio7i occurred was subtracted the volume occupied by the 
non-gaseous residue. 



IX. — NOBLE AND AP>EL S EXPERIMENTS. 9 

Remarks. 

This conclusion, although simplifying the labors of the 
experimenters, and useful for a general discussion like the 
present, is now believed to depend upon a compensation of 
errors. 

It is now believed that the solid products are volatilized 
and probably dissociated, and it is known that Mariotte's 
law does not apply to the pressures observed in guns. 

Still the latest researches lead to practically the same con- 
clusions reached by these experimenters. 

EXPERIMENTS IN GUNS. 

The experimenters found that when the gases expanded 
into a varying volume, as in the gun, results similar to those 
above described were found, vk.: 

1. Products. 

That the nature and proportions of the products remained 
the same as in a closed vessel. 

2. Working Substance. 

That the work on the projectile may be considered to be 
due to the elastic force of the permanent gases. 

3. Source of Energy. 

That the heat evolved by the non-gaseous residue main- 
tains the gases at a constant temperature during their expan- 
sion, which, therefore, is isothermal. 

This is essentially the hypothesis of Hutton, made a cen- 
tury ago. For want of suitable apparatus Hutton erred 
greatly in his deductions from this hypothesis, 

4. Theoretical Work. 

The total theoretical work of the permanent gases, when 
indefinitely expanded, was computed to be about 486 toot- 
tons per pound of powder. 



10 IX. NOBLE AND ABEL's EXPERIMENTS. 

This is nearly the result given by the table on page 7. 
Only from 13 to 20 per cent, of this work can be realized 
in practice. See note 2, page 13. 
6. Loss of Heat by Absorption. 

The quantity of heat lost by absorption was approxi- 
mately determined by plunging into a calorimeter a field 
piece, after firing from it a number of rounds in rapid suc- 
cession. 

The loss was found to vary directly with the ratio of the 
cooling surface to the weight of the charge, and also with 
the time of travel in the bore. 

It varied, per unit of weight of the powder fired, approx- 
imately as follows: 

Gun. Loss in H. ^ Energy. 

10 in. M. L. R. 25 3.5 

12 pdr. B. L. R. 100 14.0 

0.45 in. B. L. R. musket' 250 35.0 

6. Pressures. 

The experimenters confined themselves to the prediction 
of velocities. The determination of the actual intensity of 
the variable pressure during the progressive combustion of 
the powder in a volume varying with the position of the pro- 
jectile during combustion was determined in only a few 
special cases. The important law by which this pressure 
varies, upon which modern guns are constructed, was left 
unsolved. 

The methods of M. Emil vSarrau, of the ^'- D^partement 
des Poudres et Salpltres^'' which depend rather upon dynam- 
ical than chemical laws, corrected, like those of Noble and 
Abel, by experiment, are now generally followed where ac- 
curate prevision, both of pressures and velocities, is required. 

The older methods are adopted in this text, as they permit 
the presentation of some of the more important phenomena 
of fired gunpowder in a relatively simple form. 



IX. — NOBLE AND ABEL's EXPERIMENTS. 11 



DEDUCTION OF THE VARIABLE PRESSURES IN A 

GUN. 
Hypothesis. 

It has been shown in Chapter VIII. that the conversion 
of gunpowder is not instantaneous. Yet, on account of the 
difficulty of determining the circumstances of the motion of 
the projectile during the period of combustion, or x=q) (t) 
and the rate of combustion under the varying pressure to 
which the powder is exposed, or gz=/ (t) it is best to begin 
by assuming that the conversion is instantaneous, and to cor- 
rect the results of computation by experiment. See note 3, 
page 13. 

Assuming then, the proportions of solid and gaseous pro- 
ducts previously given, and that the change in pressure is 
due to the change in volume in rear of the projectile (which, 
under the isothermal hypothesis, acts like a piston moving 
with variable velocity under some external force), we may 
deduce the following relation between the pressure and the 
mean density of the products of the explosion. 

Let / represent the intensity of the gaseous pressure in 
tons per square inch, and 

Wy the weight of the charge in pounds; 

Vf the variable volume behind the projectile in cubic 
inches; 

v'f the volume occupied by the non-gaseous products in 
cubic inches; 

<^, the density of these products referred to water; 

d, the density of the gases referred to water and supposed 
to remain at a constant temperature. 

jff, the ratio -^ assumed under Mariotte's law to be con- 
stant. 

Deduction. 

From the general expression for density we have 



12 IX. — NOBLE AND ABEL's EXPERIMENTS. 



^ 0.44 wx 27.68 12.18 a/ , 

d— -. = -J- ; and 

v—v v—v 

^, 0.56 wx 27.68 , \h.hw 

d'^ -, •••^^--^7-; and 



^ 15.5 w 

" — n^' 

Multiplying both numerator and denominator of the value 
of/ by 

27.68 2.2724 



12.18 z;~ V 



, we have 



p=R ^ -. (7) 

2.2724-1.2726 -^ 

The ratio, R^ is found, by experiment, not to be absolutely 
constant; but, by selecting from Noble's experiments in 
closed vessels, suitable values of / and A in pairs, and by 
substituting these values in Eq. (7), we may obtain two 
equations, containing two unknown quantities, from which 
we find (See note 4, page 13.) 

7?=32.18 ^'=0.824. 

These values substituted in Eq. (7) give, after reduction, 
_ 1 * 

A 
Which, for convenience, may be placed under the form 

/= 1 (9) 

0.0025571 - -0.048 

w 

Equations (8) and (9) give remarkably close approxi- 
mations to all but the very highest pressures found in Noble's 
experiments in closed vessels. 

*log 0.070618 ="3.8489170. flog 0.0025571 = 3^4077557. 



IX.— NOBLE AND ABEL's EXPER1M£NTS. 13 



COROLLARIES. 

V 

1. By substituting in Eq. (9) proper values for ^= — ^>we 

may construct a curve, as in fig. 4, which will give the pres- 
sures at different points along the bore of the gun under the 
assumptions noted, page 11. 

Should the piece be chambered, the value of x\ the re- 
duced length of the chamber =.Yo\vimQ. of chamber-^ ;r t^ must 
replace its measured length. 

2. It is evident that the value of the initial ordinate is 
determined by the value of the density of loading, A. 

3. Also that, knowing by experiment the intensity of the 
maximum pressure, and the charge, we may determine 
approximately the corresponding position of the projectile. 

__ ^ [l+(/X 0.04 8)1 
Smce X — ^^py^ 0.0025571 ' 

4. Also that we may determine the charge required to 
burst a closed vessel, like an explosive projectile, when its 
resistance to rupture is known. 

NOTES. 

1. Page 13. — The experimenters ascertained that the erosion of the 
bore, caused by the rush of the gases past the projectile, increases directly 
with the factor H, and inversely with v^. 

Since modern steel guns fail rather from erosion than from bursting, it 
is possible that the large values of H, now generally sought, may be 
ultimately diminished in favor of z/q. 

That is, that the guns have a surplus of strength that may profitably 
be used to favor their endurance under erosion. 

2. Page 10.— Taking y=1390 ft. -lbs. for !« C we have 
Q=-U[= '^^TXISQO ^ ^g,^ 3 Qj. 94 ^^^^^ oi4:%Q. foot tons. 

2240 2240 

3. Page 11. X and a signify respectively the variable space passed 
over by the projectile and the variable surface of the burning grains com- 
posing the charge. Chap. XI, pp. 2, 3, 4. 

4. Page 12. — For recitation at the board the numerical values after 
Eq. (7) may be represented by symbols. 



X.— eoMStrstiON IN Alft. 



CHAPTER X. 

COMBUSTION IN AIR. 

Single Grain. 

We know from the experiment in Chap. VIII that in air, 
gunpowder burns only superficially, so that the burning 
under these circumstances of a spherical grain may be 
likened to the exceedingly rapid peeling of an onion. 

Considering, for the present, all solid grains to be repre- 
sented by their equivalent spheres, the radius of any sphere 
will be equally shortened in equal successive times, but the 
surface and the volume will vary in a higher ratio to the 
time. 

Accordingly let Fig. 1 represent the central section of 
a hom.ogeneous spherical grain burning with a uniform 
velocity of combustion which in the variable time, /, will 
reduce the original radius R, to r, and the original surface 
iS", to s. Let the time required for the combustion of the 
entire grain be r. 

Then ^: j::i?2 : ;^::t2 : (r-/)2, or 

^=^{r-t)\ (1) 

By differentiating Eq. (1) with respect to s and / we have 

It may be shown from Equations (1) and (2) that the 
curve, Fig. 2, expressing the relation s=/{f), is a parabola 
referred to a system of rectangular axes; one of which, the 
axis of times, coincides with the tangent at the vertex of the 
parabola, and has upon it the origin, O, at a distance from 
the vertex =r. 



X. — COMBUSTION IN AIR. 



The rate of change of the ordinate of the curve is the 
same as that of the surface of the burning grain. 

The summation of the successive ordinates of the curve, 
corresponding to any value, /, will be equal to the area 
O Ssf; and since the ordinates represent the correspond- 
ing successive surfaces, this area will be proportional, either 
to the mass or volume of the grain which has been burned 
up to the time /, according as the density of the powder is, 
or is not considered. 

y'' dw 
sdtj-j- =s, or the rate at 

which the mass of gas is increasing at any instant,or the 
rate of conversion, is proportional to the corresponding 
surface.* 

The total area O S r= — - — will be proportional to the 

o 

original mass or volume of the grain. 
Number of Grains Varied. 

Such a relation, once established, would be true for all 
equal grains composing a charge, and would therefore be 
true for the whole charge, but the rate of conversion would 
vary with the size of the charge as shown by curves 1 and 
2, Fig. 3. In these, 1, represents such a curve as shown in 
Fig. 2, for a single grain; and 2, the same for n grains com- 
posing a charge. 
Size of Grains Varied. 

If, in a charge of a given weight composed of spherical 
grains of a given density, the -size only, of the grains be in- 



*If the grain be not homogeneous, and burn with a variable velocity 
the rate of conversion will vary with the product of the surface, J, of the 
density, b, and of the velocity of combustion ft), or 

= J X X w. 

dt 

In this case the curve will no longer be a parabola, 



X. — COMBUSTION IN AIR. 



creased, the sum of the granular surfaces, ^ S, will be in- 
versely proportional to the radius of the grain. 

•For W=n v d, and v= — jr— .-. W= 



or^= 



3 3 ' 

3 W 1^ 

nS ' r 

or r 

If we represent by ^ the sum of the initial granular 
surfaces of a charge, and by 6 the sum of the successive 
granular surfaces of the same charge during its combustion; 
Fig. 4 may represent by curves 1 and 2, respectively, the 
relation G=f {f) for charges of equal weights composed of 
grains of different sizes. 
Objections to increasing Size of Grain. 

The effect of increasing the size of the grain is to make 
the powder relatively slow ; or, as it is called with reference 
to its action in the gun, 7nild or progressive. This diminishes 

the value of --z- by increasing the value of r. 

The objection to this will hereafter appear; it will suffice 
here to say that it may require the gun to be of inconvenient 
length. 

Alternatives. 

The following methods have been proposed for regulating 
the rate of conversion without, in all cases, increasing the 
value of r. 
Constant Rate. 

1. A constant rate would evidently be attained by form- 
ing the powder as a prism and confining the burning area to 
that of its cross section. This result is approached in the 
Zalinski pneumatic gun, in which compressed air from a 
large reservoir, expands continuously into the volume be- 
hind the projectile. Also in the steam engine. 



X. — COMBUSTION IN AIR. 



2. An approximation to a constant rate, with a small value 
of r, has been sought by forming the powder into volumes 
of which two dimensions considerably exceed the ihird. The 
French, Castan, powder and the American, LX, powder are 
so formed. 

Increasing Eate. 

The rate of conversion may be increased by causing the 
burning surface to increase: 

3. By igniting the grain from the interior, and protecting 
the exterior surface from the flame by forming the grains 
into hexagonal prisms closely packed together, fig. 5. The 
perforations are continuous flues, facilitating inflammation. 

This is Rodman's powder. 

4. By diminishing the density of the grain toward its 
center, Chap. III., or by facilitating its disruption after 
ignition. 

These cases may be represented by the correspondingly 
numbered lines on figure 6. 

COROLLARY. 

Supposing the charge to consist of n equal spherical grains, 
the proportion of the whole charge that will be burned in the 
variable time, /, may be determined as follows : 

The original volume of the charge is, F= n ^ i: R^ \ or, 
assuming, as before, that the velocity of combustion is unity, 
V=z n -^ TX r^, the unburned volume at the end of the time, 

t,v7'i\\hev,-n^7T{r—ty=,v{l—[\ - Therefore, the 
volume burned will be, z/'= V—Vf^z V\ 1 — ( 1 — - j (4) 

Similarly w' = ^F 1— ( 1— ^)' 1 - (5) 

The curve whose ordinates express the relation w' z=. f {t) 
will be of the form shown in figure 7, and figure 1, chap. XII. 



XI. — COMBUSTION IN A GUN 



CHAPTER XI. 
COMBUSTION IN A GUN. 

PRESSURES. 

Comparison to Steam. 

For purposes of illustration, the action of gunpowder, 
when burning in a gun, may be compared to that of steam 
in the cylinder of a steam engine; and the pressures,/, at 
different lengths of travel, x, of the projectile in the bore, 
may be represented by the ordinates of a curve which 
expresses the relation jf=f [x), in the manner used in the 
indicator diagram of the steam engine. 

The operation may be conveniently analyzed by dividing 
the volume of the bore into two portions, viz.: 

1st. That through which the elastic gases are being 
evolved from the burning powder, called the combustion 
volume. 

2d. That through which these gases are expanding under 
the elastic potential acquired during combustion. This may 
be called the expansion volume. 

Thus, the circumstances during the passage of the pro- 
jectile through the combustion volume correspond to the 
admission of steam to the cylinder of a steam engine, and 
the completion of the combustion to the action of the valve 
which cuts off the supply of steam. The subsequent expan- 
sion in both cases is limited by the length of the cylinder. 

This important difference exists; that the expansion, 
which in steam is treated as adiabatic (without loss 
of heat except from external work), and which, there- 
fore, leads to a loss of temperature due to the work done, 



XI. — COMBUSTION IN A GUN. 



is, in the gun, supposed, from Noble and Abel's experi- 
ments, to be isothermal^ and, therefore, under Mariotte's 
law. 

DISCUSSION. 

Hypotheses. 

In the following general discussion we will, for simplicity, 
begin by assuming that the projectile starts freely from its seat. 
We will neglect the variable volume of the liquid residue 
and that of the powder remaining unburned at any time. 

We will also assume that the inflammation is instanta- 
neous. See Chap. VIII. 
Notation. 

Taking the origin of co-ordinates at the origin of motion; 
X will represent either the path of the projectile or the 
volume described by the translation of its maximum crosr 
section. 

The volume of the chamber, ^, or the initial volume, is 
composed of two volumes, viz.: 

c, the volume actually occupied by the charge of powder 
including its interstitial spaces. 

c\ any excess of volume besides that required to hold 
the charge. Therefore, k=zc-\-c\ and, for the reduced 

k 
length of chamber^ we have x, -=l ^ , in which r is the 

radius of the bore. We shall first take c' = O. 

Let w represent the weight of a charge of powder which 
will be consumed in a time r, and let w' be the variable weight 
of w converted into gas at the end of any time /. 

Let (S represent the corresponding sum of the burning 
surfaces as in Chap. X, and '2 the sum of the initial sur- 
faces. 

Let / represent the variable intensity of the gaseous 
pressure per unit of area on the base >f the projectile; and 



XI.— COMBUJ^TION m A GUN. 



assume any particular value o. / to be uniform throughout 
the volume occupied by the gases, the density of which is d. 

Let/ be taken in such units that R^ Chap. IX, be equal to 
unity. 

Let W represent the weight of the projectile, the radius 
of the cross section of which is r\ the variable velocity of 
which, in the bore is v\ and, at the muzzle of the gun is V. 

Let q and Q represent the quantities of work done upon 
the projectile to give it the velocities v and V. 

FORM OF PRESSURE CURVE. 

Upon firing the charge the combustion volume is gradu- 
ally filled with gas, the density of which will vary directly 
with w' and inversely with x-\-c\ so that we may write 

w' 

Differentiating this equation, considering /, w* and x as 
variables, and dividing through by dx^ we have 
dp __ 



dx x-\-c 



1 i dw* w* \ 
'^c\dx x^cX 



(2) 
(3) 



But, since q=f p dx^ 

dp _ _1_^ / dw'—dq \ 
dx ~ x-\-c \ dx J 
Or, dividing both numerator and denominator of the 
expression in the parenthesis by dt and remembering that 
dw' 



dt 



Similarly, 



dp _ 1 / dq \ 

dx '~ {x^c)vy dt )' W 

dp 



No simple law has yet been discovered connecting (T, x 
and /, and these equations cannot, therefore, be integrated; 



XT.— COMBUSTION m A GUN. 



but, remembering that (T is a decreasing function, and q 
an increasing function of /, a conception may be had of the 
form of the curve, the ordinates of which express the 
relation /=/ (^). 

The inclination to the axis of X will be greatest at first 

when 6 is large, and x and ~- =p v are small. It will be 

Oy or / will be constant, when the gas is evolved just fast 
enough to compensate for the increasing volume. From 
this point the conversion is not rapid enough to keep up 
the maximum pressure, so that the pressure will fall off 
until a=.Oy as at «, Fig. 1, from which point the curve will 
be an hyperbola with the axis of X as an asymptote, since 
p becomes equal to a constant, w, divided by x-\-c. By 
the law of continuity, a should be a point of inflexion and a 
point of tangency between the combuscicn and the expan- 
sion curves.* 

The same results will follow when / is taken =/' {t), ex- 
cept that the inclination of the tangent to the curve will 
vary more gradually. 

I. PRESSURES DURING COMBUSTION. 

Effect of Size of Grain. 

Although we do not know the law which, in the gun, con- 
nects (T=/(/) and x = Qf (/); experiments with Noble's and 
Ricq's apparatus demonstrate that, when nearly equal charges 
of powder, a and b, in which H^ > Z^^ are fired ; for small 



♦The parenthetical expression refers to the relation between the poten- 
tial energy of the unburned powder and the kinetic energy of the projec- 
tile ; for n, the potential energy of the charge must always be equal to 
7r = /(CT), that residing in the unburned charge; -]- q=f^ (v), the work 
already done at any instant; -\-e=/^^ (/), the work which the elastic 
potential of the gases is capable of doing; or H =7r -j-q-\-e. 



XI. — COMBUSTION IN A GUN. 



values of x and /, cp (/) changes but slowly for considerable 
variations in/" (/). 

The small change in the form of cp (t) for a given change 
in the form of / (/) is probably due, on one hand, to the 
relative constancy of the initial resistances to motion, or 
the molecular work (Michie, Art. 25), and on the other hand, 
to the great changes in / {t) resulting from the cumulative in- 
fluence upon the velocity of combustion of high pressures 
when (7 is large. Chapters VIII., X. 

If, therefore, during the critical period of combustion, we 
assume that qp (/) is nearly constant for all sizes of grain; 
V, and therefore ^, may be taken as independent of o. Con- 
sequently, Eq. 4 shows that during combustion, the inclina- 
tion of pressure curves corresponding to different values of 
Z will be an increasing function of a ; or for equal charges, 
the smaller the grain, the steeper the curve. Similar reason- 
ing shows that it will also be higher. 

Experiine7ital Illustration. 
This may be re'presented by fig. 2, derived from Noble's 
experiments, in which a represents, by its ordinates, the suc- 
cessive surfaces of a charge of fine-grained powder burned 
in the air, its initial portion only being represented. The 
curve a' shows the effect produced upon its burning by con- 
finement in the gun. Let b and b' similarly represent the 
varying surfaces of an equal charge of coarse-grained 
powder. Let a and /3 be corresponding curves representing, 
by their ordinates, the velocities acquired by the projectile at 
any time, /. For any time /, the area under a' or b' = 

J a dt=w' ; and similarly the area under a ox (i=J vdt—.x-^c. 

Under the circumstances named, although Z^=*^ Zy,, the 
curves a. and |3 were nearly coincident in their initial por- 
tions. These, which we shall term the v curves and the a 
curves, have the axis of time m common. 



XI. — COMBUSTION IN A GUN. 



At any time /, which is less than tb, the time required for 
the combustion of the powder ^, the ratio, =/» is less 

for the coarse grained powder than for the fine. At t^ ^^d 
Tb expansion begins ; at r^ the pressures from the two pow- 
ders will be nearly equal to each other, since the same weight 
of powder in each case is burned in nearly equal volumes. 

Similar effects would follow the changes in a, indicated in 
Chap. X., from whatever cause the rate of change of o was 
varied. 

The best results would be attained when both the <j and 
V curves coincided in such a line as ^, fig. 2, since we 
would then have the constant pressure sought for in the 
ideal gun. 

The effect upon pressures of varying the size of grain, or 
the rate of burning in charges of equal weight, would be 
represented by the curves a, b^ k, in fig. 3, in which the nota- 
tion of fig. 2 is preserved. 

Additional Illustration, 

The principle is illustrated in figure 10, in which curves a 
and b (which to avoid confusing the drawing are omitted), may 
be imagined to result from Equation (5), Chapter X, and a' 
and b' to be constructed from a and b^ in the manner indi- 
cated in figure 2. The curves a and ^ express the relation 
x=f' (/) as in figure 2 they expressed v=.f{t). 

The ordinate t y' represents the proportionate part w', of 
the original weight of the charge, w^ (represented by O 7v), 
that has been burned in the time O t\ and / z' the volume, x, 
through which the projectile has moved in the same time. 
Similarly for the curves b' and /?. 

The line ^^ is parallel to O T^ and at a distance from it, on 
the scale of the axis JT, that is proportional to the volume of the 

chamber.. Then^p-p-^ = -^ = ^=A.- and similarly 
for the curves b' and ^. 



X!. — COMBUSTION IN A GUN. 



In figure 2 it is not possible to represent the constant of 
integration, c, 

2. PRESSURES DURING EXPANSION. 

The locus of the pressures at the end of the several com- 
bustion periods is the hyperbola H, fig. 3, the intersection of 
which, with the axis of P^ is at a height (9/, corresponding 
to 43 tons per square inch, and the parameter of which de- 
pends upon the weight of the charge. Thus, the hyperbola 
H' would be the locus for a charge greater than w, and its 
vertical asymptote would be at a distance from 6?= —Xi—c 
See figure 5. 

Remarks. 

1. The relative constancy of the v curves, in spite of con- 
siderable variations in /, may be explained by considering 
the gunpowder as a reservoir of potential energy. In this 

— ^ — J , SO that v=J\^w')y while we 

have seen that/=/^^(w'). 

2. It is probable that the work done during combustion 
is proportional to the weight of the charge. 

ADAPTATION OF POWDER TO GUNS. 

The preceding discussion shows that if the size of the 
grain remains constant, the pressure increases with the size 
of the charge. 

In order to compensate for this, General Rodman pro- 
posed to increase the size of the grain as the caliber of can- 
non of the same class increased. 

This is the basis of the modern practice requiring special 
powders for special guns. 



XI. — COMBUSTION IN A GUN. 



PASSIVE RESISTANCES. 

Returning to fig. 1, we see that the area limited by the 
pressure curve, the axis of X, and the muzzle ordinate at w, 
will represent the work done by the powder under the cir- 
cumstances named. 

The greater portion of this work appears in the kinetic 
energy of translation of the projectile; and, for simplicity in 
the following discussions, all the work will be considered to 
have been so transformed. 

The difference between the work of the pressures and the 
energy of translation, which, in practice, may amount to 
about ten per cent, of the former, is due to the work of the 
passive resistances ^ including the waste. 

Eesistances. 

The work of these resistances is equal to the sum of the 
following quantities of work: 

1. That done in giving rotation to the projectiles in rifled 
guns and in causing recoil. 

2. That done in permanently deforming the projectile and 
the gun. The former is practically confined to rifled pro- 
jectiles and is greatest in breech loaders. 

3. That done in overcoming the friction of the projectile, 
and in distributing the charge in the form of gas through- 
out the bore. 

Waste. 

4. The waste is due to the absorption of heat by the walls 
of the gun, and to the escape of the gases past the projectile 
and through the vent. 

Graphical Representation. 

So that if we take a pressure curve, as in fig. 4, and draw a 
line R R\ so that the area under it, corresponding to any 
length of path x, shall represent the work of the passive re. 
sistances during the motion of the projectile over that path, 



XI. — COMBUSTION IN A GUN. 



the segment r/, of any ordinate x p, will represent that por- 
tion of the total pressure which gives acceleration to the 
projectile and imparts to it kinetic energy proportional to 
the area included between the two curves and any limiting 
ordinate. 

Remarks. 
Band. 

In breech-loading guns the initial resistance is consider- 
able until the rotating band has entered the rifling; there- 
after the resistance diminishes rapidly. 

Example: In a 9.5 in. B. L. R. a charge of over 4 pounds 
of powder failed to move the projectile; but a slight increase 
in the charge gave it considerable velocity. 
"Waste. 

The loss of energy from absorption of heat by the gun 
increases with the slowness of the powder; since with slow 
powder the velocity of the projectile is less at the moment 
of maximum temperature or pressure. 

It varies inversely with the calibre, since with charges of 
the same proportions the weight of the charge varies with 
r*, while the surface varies nearly with r^. 

The escape through the vent probably increases with the 
slowness of the powder. 

Instantaneous Pressure. 
Variability. 

From the discussion, Chap. VII., it is evident that the pres- 
sure at any instant throughout the volume in rear of the pro- 
jectile is not uniform, but increases toward the bottom of the 
bore, as represented by the variable line/o/- Fig. 4. 

Neglecting the passive resistances, the intensity of the 
variable pressure at the bottom of the bore, generally known 
as/o> can, by analysis, be shown to be very nearly equal to 



/ 



(w \ 



10 



XI COMBUSTION IN A GUN. 



Considering the passive resistance/o is taken =// 1 + yTvi- 

Supposition. 

For an elementary discussion, like the following, such 

differences in the instantaneous pressure, and the effect of 

the passive resistances, once understood, maybe neglected. 

So that the pressure at any instant upon the bottom of the 

bore will be assumed to be that exerted at the same instant 

on the base of the projectile, and all of it is supposed to be 

utilized in giving motion to the projectile. 

JV 
The difference, p n r' a, evidently tends to compress 

. . . ^ 

the projectile in the direction of motion, and its effect will be 

most felt at the base of the column of metal moved. 

Except in the next discussion, in which actual free vol- 
umes are considered, the origin of co-ordinates is always 
taken at the origin of motion; viz., at that section of the 
bore occupied by the base of the projectile when the gun is 
fired. 

WORK OF FIRED GUNPOWDER. 

It is not necessary in practice to separate the work of 
combustion from that of expansion; but the total work which 
may be expected from a given charge of powder may be 
determined in the following manner. 
Total Potential Work. 

In fig. 3 the area included between the ordinate O P^ the 
axis of X, and the hyperbola H at infinity, will represent 
the total amount of work which this charge could perform. 
Calling this i2, we see, from Chapter IX., that expressing, 
as is usually done, work in foot-tons, and w in pounds, 

/2=486 w. 
Actual Potential Work. 

If, instead of expanding the powder gases to infinity, we 
limit the useful work of the expansion by placing the muzzle 



XI. — COMBUSTION IN A GUN. H 



as at m^ we shall have an area which will represent the 
maximum potential work under the conditions existing in 
the gun. 

This, which in practice is not much over — , we will call Q. 

Effective Work. 

Now, if we fire the charge w in a gun, we shall give a 
certain velocity F to a projectile W. Calling the amount 
of kinetic energy so realized E^ we have 



E=. 



2^x2240 
The ratio, -— = F, is called the factor of effect. It is 

used, as hereafter explained, in anticipating the results of 
certain changes in the piece and ammunition. 

Fig. 3, shows by the triangular areas above the curves, 
a, ^, k, the principal reason why 7^ < 1. 

F is further diminished by the passive resistances. 

MEASURE OF Q. 

To deduce a formula for the potential work of the 
powder gases when expanded in a gun of a definite length, 
or the equivalent of the area Q^ we use the general equation 

^—^dx. (6) 

Substituting the ;i^alue of /, from Eq. 3, Chap. IX, and 
for brevity replacing 0.0025571 by «, and 0.048 by by we 
have, since all linear dimensions are given in inches, 

G" (inch-tons) = ^ 




na d* 



12 



XI. — COMBUSTION IN A GUN. 



(2" (inch-tons) ='^ ' '^^ 



Takinrj, in this case, the origin of co-ordinates at tne 
bottom of the bore, integrating between x^, and x' , corre- 
sponding to O' O and O' m^ fig. 1; substituting the value 

of a^ and remembering that Q= ■^— , we have, 

^'-23.9 ^3 

e= 75.04 tt/, log ~ . (7) 

^,-33.9 -, 

Volumes of Expansion. 

The subtractive term above, appears from the form of the 
equation and can be shown to be the reduced length of the 
residue,* or 

/>=33.9^; (8) 



pand x^/—x^—p: — =z n ^ number of 

volumes of expansion, an important characteristic of a gun. 
It is convenient to remember that p=: about -j^ the length 
of the cartridge, if its diameter =d above. 

Equation 7 may, therefore, be written under a form con- 
venient for general discussion. 

(2=75.04 w. log«. * (9) 

The calculus shows that the curve, the area between 
which, the asymptote, and two ordinates is proportional to 
the logarithm of the extreme abscissa, is an hyperbola, 
which is the result reached, page 4. 

* For the smokeless powder referred to in Chapter III, p will be prac- 
tically = 0, n will diminish, and so will /o for equal values of w. The 
effect, as hereafter discussed under Air spacing, will be to make the powder 
more progressive ; unless the powder belongs to the class of high explo- 
sives and its explosion is of a high order. 



XI. — COMBUSTION m A GUN. 1^ 



Consequently if, as in fig. 5, we assume axes of P and 
iV", we may construct various hyperbolas depending upon 
the value of w^ such that the areas under them will give^ 
the corresponding values of Q. 

VARIATIONS. 

1. In Weight of Charge. 

The hyperbolas intersecting at the point P, Fig. 5, and 
Equation 7, show the effect upon x,; x' \ x,,; x"; p; n; 
Q ; and /, resulting from variations in w. 

Inspection of the figure shows that an increase of 7Cf to 
7£/ =: -f 7i>, decreases n from about 12 to 7, or about ^ ', 
the total length of the bore x' =z x" remaining constant, as in 
a muzzle loader. 

Owing to the effect on n of variations in w, Q will not in- 
crease in direct proportion to w. But, in a given gun, log 
n diminishes so much less rapidly than w increases, that we 
may for simplicity assume that n is constant; and, taking a 
constant ratio between n and x, we may replace the axis of 
iV^by that of X, and complete the figure by drawing upon 
it combustion curves, as in Fig. 6, so that for the same weight 
of charge the areas under the combustion curves are equal, 
without regard to the size of grain. See Remark 2, page 7. 

2. In Size of Grain. 

The curves a' a" , refer to different weights of the same 
kind of fine grained powder, which are supposed to be 
burned through at about the same point of the bore. Curve 
a", refers to a weight w of coarse grained powder. 

Consideration of Fig. 6, shows how, by increasing both 
the weight of the charge and its inherent progressiveness, 
we may obtain a pressure curve, the work area under which 
may equal and even exceed that due to the fine grained 
powder, without incurring the risk attending the high pressures 
to which it gives rise. 



14 XT.— COMBUSTION IN A GUN. 

In other words, we approach the conditions required in 
the ideal gun, by effectively diminishing the value of n. 

For, comparing curves a" and b" ^ figure 6, it is evident 
that the latter is the more progressive, or more nearly parallel 
to the axis of X, and that this results from expansion begin- 
ning further down the bore. Neglecting the areas under the 
combustion curves, the inclination of which in the diagrams 
is purposely exaggerated, the effect is practically the same as 
if the powder had been instantaneously burned in a volume, 
c -\- c', greater than c, page 2, by the volume through which 
the projectile had moved before expansion began. We would 

x' p 

then have n' =: , , — < n. See Air Spacing, 

x, + c'—p 

3. In Length of Bore. 

While, in all cases in practice, an increase of O m increases 
Q and F, the proportionate advantage from the increase of 
O m increases with the progressiveness of the powder. 

The limit of useful increase of O mis determined by the 
intersection of the line of pressures with that of resistances. 
Fig. 4.* 

In many works on Gunnery the importance of Om^ or the 
path traversed by the base of the projectile in the bore of 
the gun, is overlooked; or it is left to be inferred from the 
total length of the bore. 

In the more recent and advanced works it has a specific 
symbol u by which it will be hereafter recognized. 

AIR SPACING. 
Variations in A. 

We have so far assumed the powder to be fired in its own 
volume. If we assign to the charge a volume greater than 
that required to contain it by the volume ^', page 2, the 



*This applies to small arms. For heavy cannon the increased weight 
of piece resulting from the prolongation of the bore, can generally be 
used to better advantage elsewhere. 



XI. — COMBUSTION IN A GUN. 15 

value of A will diminish. Eq. 8, Chap. IX., shows that the 
initial pressure will also diminish, and so, under given con- 
ditions will Q. In such a case, Eq. 1, will take the form 

/= j — , and the curve expressing the relation 

x-\-c-t- c' 

p =/ {x) will be such as shown in fig. 7. 

Curve 1 expresses, by its ordinates, the varying pressure 
when A is large, and curve 2 the same function when A is 
small, the weight of the charge being the same in both cases.t 

It will be observed that the effect of air spacing is princi- 
pally felt when c^ is large, compared with x^ that is, when cs 
and/ are relatively large. 

Also, since by differentiating Eq. 1, regarding w' as a 

df) 11) 

constant and x + k=-\^ we have -^ = r-^^; the inclination 

aA. Ar 

of curve 2, will be less than that of curve 1. The values of 

Q and B will therefore both be smaller for curve 2. 

Increase of Charge. 

If u is fixed, this effect is compensated for, as before, by 
increasing w. This produces the effect shown in the dotted 
curve, 3, fig. 7. 

APPLieATIONS. 

Air spacing is principally applied to muzzle-loading can- 
non on account of the necessary limit to their length imposed 
by the requirements of loading. It results spontaneously from 

t To familiarize himself with the principles involved, it is recommended 
that the student construct curves 1, 2, 3, as follows : 

1. Assume a maximum pressure of say 24 units and<:=l; c^ = o', 
10=1; thenfor jr = l,/ = 12; for x=2, / = - =8, and so on. 

2. Take c^ =1.-, /& = 2; w=:l, as above; then for x = o,p^=12i 
for x = 2fp = Q, and so on. 

3. Take^=l and w = 1.5; then for x = o, p=-=18', forjr=l, 
/ = 12, as in No. 1; forx = 2, /=9 (greater than No. 1). No. 3 will 
continue above No. 1 to oo. The powder is more progressive, and n is 
decreased. 



16 XI. — COMBUSTION IN A GUN. 

the ease with which their projectiles, particularly those 
which are spherical, take up their initial motion. It was 
probably to diminish this that the sal^of, a cylindrical block 
fastened to the rear of spherical projectiles, was formerly 
employed, although other reasons are generally assigned for 
its use. 

Until about 1880, when the EngUsh government began 
to adopt exclusively the breech-loading principle for heavy 
cannon, air spacing was largely employed for s/wrf, thick 
muzzle-\oa,dmg cannon, firing large charges of ^uick-huYn- 
ing powder. It was secured by making the diameter of the 
chamber greater than that of the bore. This was objec- 
tionable in sponging and it weakened the gun. 

It was made constant by providing the projectile with 
stops, which held it at an invariable distance from the bottom 
of the bore. But this, although beneficial in preventing the 
great variations in pressure and velocity which, from care- 
less loading, are apt to occur in ordinary muzzle-loading 
guns, increases the length of the gun in the region of its 
greatest diameter. 

It is still employed to some extent in breech-loaders, but 
is yielding in importance to the means now employed for 
regulating the combustion of gunpowder. 

EFFECT OF THE ROTATING DEVICE. 

If the initial motion of the projectile be restrained by the 
compression of the rotating device,/ will have an initial 
value at least equal to the resistance offered to deformation, 
and, since the powder is burned under higher and more 
constant pressures, n will be greater and more constant 
than when the projectile is free to move. 

ADVAIsTAGtS OF BREEuH-LOADING GUNS. 

General Advantages. 

1. The simplicity and exactness of the method by which 
the value of n may be regulated. 



XI. — COMBUSTION IN A GUN. 17 

2. The ease with which u may be increased without inter- 
fering with the operations of loading. 

3. As will be hereafter shown, the compressible pro- 
jectiles used in breech-loaders are more accurate than the 
loosely fitting projectiles employed in muzzle-loading guns. 

In spite of the greater simplicity of construction and of 
operation of muzzle loaders, these advantages have com- 
pelled the adoption of breech-loading cannon. 

Tactical Advantages. 

The tactical advantages of breech-loaders are also greater. 
Among these are — 

1. Greater facility in securing cover for the piece behind 
defenses, and for the gunners behind the piece. 

2. Less danger and difficulty in loading, since but one 
charge can be inserted at a time, and the operation of spong- 
ing is less important than with muzzle loaders. 

3. Greater facility in examining and caring for the bore. 

4. Greater facility in adjusting the charge or fuze after 
loading. 

5. ImmovabiUty of the projectile in marching. This per- 
mits batteries to come into action rapidly, when under fire. 

6. The rapidity of fire is increased for large pieces. 

The price paid for these advantages is the difficulty of 
getting officers and men capable of working the cannon with 
sufficient care. 

OBJECTIONS TO INCREASING WEIGHT OF 
POWDER. 

The preceding discussions show that we compensate for 
small values of 7i by corresponding increases in the value of w. 

The objections to this are as follows. 

1. We increase the waste of powder, as the steam en- 
gineer does that of his coal by failing to work his steam ex- 
pansively. This may be of importance when storage capacity 
is limited, as on ships and in the field, and it tends to dimin- 
ish the value of ?y, hereafter explained. 



18 XI. — COMBUSTION IN A GUN. 

2. The work done in distributing the gas throughout the 
bore increases with the weight of the charge and the length of 
u. Some charges now weigh half as much as the projectile. 

3. We increase the tension of the gases within the gun at 
the instant of the departure of the projectile. This tends 
to accelerate the recoil and to perturb the flight of the pro- 
jectile ; since, owing to their small mass, the gases leave the 
gun with a higher velocity than that of the projectile. 

4. Considering the gun to consist of a number of staves, 
like those of a barrel, the moment of the pressures about the 
breach is increased on account of their greater level arm. 

5. Variations in / and «, due to accidental variations in 
the velocity of combustion, may endanger the safety of the 
piece or affect its accuracy. 

IGNITION AND INFLAMMATION IN GUNS. 

The importance of these phenomena has largely decreased 
with the adoption of the breech-loading principle. 

When muzzle-loading cannon, firing free projectiles with 

charges of fine grained angular powder were generally used, 

.1 . . time of inflammation , 

the ratio -— ^ , — was large. 

total time of conversion 

To reduce this as much as possible, so as to increase the 
value of n^ the charge was ignited near its middle. It was 
found that ignition in rear tended to waste energy by moving 
the forward portions of the unburned charge ; while that in 
front reduced the velocity by the premature movement of the 
projectile. 

With breech-loaders the charge is always inflamed before 
the projectile has moved. 

The shape and size of the grain and the use of a special 
priming of quick powder placed near the vent, reduce the value 
of the ratio of times above referred to so much, that the 
position of the vent is determined by other considerations. 



XI. — COMBUSTION IN A GUN. 19 

MEASURES DEPENDING UPON THE MUZZLE 
ENERGY OF THE PROJECTILE. 

1. MILDNESS OR PROGRESSIVENESS. 

P =: / TT r^ is called the variable total pressure. 

In this, and in subsequent similar expressions, r is expressed 
in the same linear units as those of the area upon which / is 
estimated. 

When/ has its maximum value, as indicated by the pres- 
sure gauge, and taken = /„ ; the maximum total pressure is 
P' = x' p', Fig. 8. 

The area under the pressure curve divided by u gives the 

mean total pressure P,-=^ — = m p,. 

u 

The effective length ox u' = — = O x". 

Therefore, if we represent the following ratio by ju, we 
have, since E = P' u' = P, u, 

^ = ^^'!L^^^ ^^' . (10) 

^ P' u P' u ^gp.-ar'u 
in which /^ and JVare expressed in the same units, and g, u 
and Fin the same units. 

This coefficient /x, which measures the ratio of the area 
under the curve to that of the circumscribed rectangle, may 
be taken as the measure of the mildness or progressiveness 
of the action of the gunpowder under the circumstances of 
any particular case. 

The limit of the ratio for all ordinary powders is evidently 
unity, and would be reached only in the ideal gun. 

2. ECONOMY. 

-p 
7) = — is a valuable datum for comparing the economy or 

w 

efficiency of various powders. 






^0 XI. — COMBUSTION IN A GtjM. 

It appears from figure 3 that the greater is the efficiency, 
the greater is the maximum pressure ; or that the violence of 
gunpowder increases with rj. Also from figure 2, that the 
smaller the value of r, or the quicker is the gunpowder in a 
given gun, the larger will be the value of t]. 

It would be more consistent to follow the method adopted 
for jLt, the value of which is independent of any particular 
metrical system \ but in order to avoid dealing with large 
numbers, and because of the general use of the term " foot- 
tons of energy per pound of powder," we shall write 

3. GENERAL COEFFICIENT. 

The preceding discussions show that all expedients intended 
to increase the progressiveness of powder decrease the muzzle 
energy resulting from the conversion of a given weight of the 
explosive ; or decrease rj. 

Thus, when, as in figure 3, we increase the size of the grain, 
or vary its form, composition or density so as to increase r ; 
or when, as in figure 7, we diminish /^ by decreasing A, we 
decrease the Factor of Effect ; and therefore, in order to ob- 
tain the muzzle energy required, we must increase the weight 
of the charge, as shown in figure 6. 

In order to compare the performance of different powders 
fired under the same conditions, or of the same powder fired 
under different conditions, it is proposed to use a general co- 
efficienty known as x '• which, since fi and r] are both desir- 
able, will be proportional to their product ; and which, since 
they tend to vary inversely with each other, will have an 
approximately constant value. 

This relation may be expressed by writing 

X-iin= ^^mp.TTiP uw' ('^^ 



XI. — Oo^rBusTloW in a gun. 61 

It will be hereafter more fully discussed. 

4. STRENGTH OF GUN CONSTRUCTION. 

// = -j^ , in which IV' is the weight of the gun (in the 

same units in which IV, the weight of the projectile, is expres- 
sed) measures the height through which the gun would have to 
fall in vacuo to acquire energy equal to that residing in the 
projectile at the muzzle of the piece. 

Thus the old 10 in. S. B. C. I. gun had a value of ^ = 300 
ft. When strengthened by a rifled steel tube that reduces its 
caliber to 8 in. we have the "converted" 8 in. Rifle, for which 
A is about 350 ft. 

For the new 8 in. B. L. R. Sfee/, h is nearly 500 ft. 

6. FACTOR OF EFFECT. 

The meaning and derivation of this have already been 
explained. 
Use. 

It is used for anticipating the effect of changes in the 
interior form of a piece, or in its ammunition, upon the 
muzzle energy of the projectile. 

It differs from the use of x ^"^ its factors in taking no 
heed of the maximum pressure involved in the result. 
Conditions. 

It is necessarily assumed to remain constant during the 
variations, the effect of which is sought; and consequently, 
the conditions under which it is employed should be as 
nearly alike as circumstances will allow. 

These conditions relate to the type of gun, of powder, 
and of projectile employed • 

Owing to the greater constancy of A, and to the high 
initial pressure required to move the projectile from its 
seat, it is better adapted for use with breech-loading than 
with muzzle-loading cannon. 



M. L. R. 


B. L. R. 


30 


60 


50 1 




65 

75 


^ 80-85 


85 





22 XI. — COMBUSTION IN A GUN. 

The factor of effect increases with the size of the gun, as 
seen by the following table, giving its approximate value, 
in certain individual cases. So much depends upon the kind 
of powder used that only the most general conclusion can 
be drawn: 

Factor of Effect Per Cent. 

Muskets, 
Mountain Guns, 
Field " 

Medium " 
Heavy " 

APPLICATIONS. 

1. Variations in w and a . 

1. Suppose it be desired to estimate the change in the 
muzzle velocity to be expected in a given gun from certain 
charges in a/ or A. 

The values of E and Q, under known conditions, have 
been determined; and therefore, 

F= -yr is known. 

Determining, from Eq. (7), Q' under the new conditions, 
we have-£''=i^ Q'. On firing we should find approximately — 

V=JJEl^. (13) 

2. Untried Gun. 

2. Suppose that we desire to estimate the muzzle velocity 
of a given projectile to be fired from a new and untried gun, 
of which we have only the drawings. 

We select the record of some gun of as nearly the same 
type as possible, assume F=F\ and proceed as before. 

3. Dimensions of Guns. 

3. The inverse problem may also arise; viz., to determine 
the interior dimensions of a gun of any required power. 



XI. — COMBUSTION IN A GUN. 23 



Eq. (7) may be placed under the form — 

w 

Q=l!6Mwlog (l4) 

^,-23.9,-^ 

The calibre and the density of loading, A, are always 
assumed, the former depending upon the service, and the 
latter upon the strength of the gup; therefore, since 

27.68 w 



A = 



V=7C — X,, 

110.72 «; (15) 



' TT ^2 A 

We have, therefore, two problems: 

1. Assuming u to find the necessary values of w and x^, 

2. Assuming iv to find u. 

The difficulty of simplifying an expression of the form 
of Eq. (14) requires these solutions to be made by trial. 
In the first case, taking F from some similar gun, we have 

01 =■ —=r- Then, assuming successive values of w, we insert 

them and the corresponding values of x^, determined from 
Eq. (15) into Eq. (14) until a suitable value of Q^ is obtained. 

In the second case, we proceed as before, substituting 
successive values of u. 

The initial approximations to the value of u will be facili- 
tated by reference to the value of n, usual in guns of the 
type proposed. 

EXAMPLES FOR PRACTICE. 

1. The 3.20 B. L. W. I. Chambered Rifle, in which x,^ 
12 in.; u= 56.1 in.; 3 lbs. I. K. powder = ze/, gave to a I'Z 
lb. projectile, F= 1548/.^. 



^4 XI. — COMBUSTION IN A GUN. 



Determine its factor of effect; 

j,_ E _ 199.3 _ 

2. Estimate V for a 13 lb. projectile to be fired from 
the new 3.20 B. L, Steel Chambered Rifle with a charge of 
3.75 lbs. I. K. powder. 

From the drawings we find that the volume of the cham- 
ber, which is a truncated ellipsoid terminated by various 
cylindrical and conical surfaces, when diminished by the 
volume of that portion of the projectile which lies within it, 
= 123.157 cubic in. Similarly, the length of the rifled por- 
tion of the bore, when increased by that of the projectile 
lying within the chamber,^ 73.24 in. Therefore, ^^= 15.31 
in., x' = 88.55 in; and in the case supposed n = about 12 as 
before. 

We find (2' = 303.9 ft.-tons, ^=247.4 ft.-tons, and 
F=1657/.J. 

By experiment, F= 1662 f.s. 

The difference falls within that usually found when all 
the conditions are as nearly constant as possible. 

DISCUSSION OF THE COEFFICIENT X. 

A study of many records shows that when the conditions 
of loading approach those sanctioned by experience, the 
value of X expressed in the units assumed varies from about 
24.0, when the powder is so quick* with relation to the gun in 
which it is to be used, that the weight of the powder is only 
about one quarter the weight of the projectile ; to about 35.0, 
when the powder is so slow that 7a may be safely increased 
to about one half the weight of the projectile. 

* The remark on page 6 shows that the same powder may be quick in 
some guns and slow in others. Thus the powder suitable for a field 
piece would be too slow for a musket, and too quick for a siege piece; 
and in two siege pieces of the same caliber, this powder would be quicker 
in a gun, than in a howitzer or mortar. 



XI. — COMBUSTION IN A GUN. 25 

It is rare to find a value of x ^vith any form of black pow- 
der greater than 28.0; while with cocoa powder it often 
approaches 35.0. Furthermore, these values approach con- 
stancy, as will be seen from the table on following page. 

The approximate constancy of x enables conclusions to be 
drawn from otherwise perplexing data. Thus, in the 7.0 in. 
Howitzer in Table I., it might be difficult to decide which 
was the better powder, L. X. B. or I.. K. K.; but the values 
of X show that the former is to be preferred. 

If we assume axes of ?/ and fj, as in fig. 9, we may refer to 
them as asymptotes certain hyperbolas which will limit all 
reciprocal values of rj and ^ for each kind of powder. Thus 
powder /^, for any assigned value of 7] or fi will give a higher 
value of [J, OT rj than powder a. 

0( the two principal ballistic data, viz.: Fand /„, the 
former is much more easily and certainly obtained than the 
latter. Indeed, unless the pressure gauges are carefully pre- 
pared by experienced observers, their indications are fre- 
quently mconsistent. 

Therefore, a known value of x ^'^^Y be employed to check 
the records of the pressure gauges, or to replace them; for, 
having observed V, we have 

^" ;^ 2240 ^^77^/^ 7/ ^ ^ 

Also, having ascertained by experiment the value of \i^ or of 
7\ for any powder of which we know the coefficient x^ ^^^ may 
estimate the weight of the charge of that powder required to 
give to a projectile of any desired weight the maximum 
velocity which the limit of pressure imposed by the construc- 
tion of the piece permits, or 

The density of loading will be regulated by this value oi p^. 
As will be shown in Chapter XII., the value of X-, for the 



26 



XI. — COMBUSTION IN A OUN. 







Sphere Hex'l powder. 
Converted gun. 
Steel gun. 

Flat powder. 

Black Prism. 

Hexagonal. 

Reported "good." 
Reported "good." 
Rep. "entirely too quick" 
Rep. "entirely too slow." 


^ 


'^o:rrt-iM<Ma:QOOor'Cooscoco(MTrioocc<M 


(M (M CI C-l (M <M C^l (M (M Ol (M (M (M (M fM CO CO CO CO 


5r 


OiO(M-«^iCOQ00iOt^OC00i0i»r5i0.«OO 

oooi-ioooitooiCiTt^inTfmt^co'oicot^TtiQO 


a_ 




< 


i-HOOOt-OOOiOOOOOiOOC<IO-<fCO 

'X)ooiOin)0?oor-oooo(Mio<x>OTj<T(i 

(Mt-kOOOOOS-^OO-VOiC^rHCDCDlOOOtD 

tooDOoso^-rjiascoiooocooot-fMeoocooo 

(M(MCO(MCOC0CCC0COr-i(M(M(MCqcOC0COC0<M 


^ 


t-OCCOOOiOiOOlOCOt'tftOSOOiOT-Ht-CO 
«OrHCOC0C0Tf<(MtOtOTtiO5(MQ0C0<X)<MC0C0C0 


PL. 


icooooooooio»a»rsicoo 
ocoeocoincocotoioooooocoosososr-i 

rH ri C^l (M (M CO 


pi 

g 


9 


COOOlOOOOOOOCTOt-' 

lo ift ift in o o 

lOCOCOCOCOCOfMiflTtitDOiOSOSCOTfOOOr-l 




: : i : : i^'.i : i ! : : i : :** ; ; 

M w w w w >< ^ 'i ^ >< >< ^ wV >^ izi ^' <i p=3 

vj k4 fj KH* w h4 c» S 6 J J J J h k cu d>Q^ d» 




S 


3 


urj in u'. o o CO o lo »o o 

COOOCOCOCOCO-^TtiTtiOOOOrM(M''<!lHTj<-<:j3TlJ 
(M ^ (M (M (M (M ^ (M (M -< — r-H r^ — -*(?} (M -M (M 


8 


ITS lO iQ O 
lft-X)(M(M(M(MOOQOOOQOOOCOOOOOt-t-C-l> 


■^tOCOCOCOCOOSOSOCOCOCOCOCDOlOlClOlO 


'«.S 


coeococococoidu^int-^r^iT-t^ooQOGdGOOOGO 


^ 


3 





XI. — COMBUSTION IN A GUN. 27 

same powder fired in the same gun, will increase as the ratio 
— mcreases ; but a nearly constant expression called 11 will 

result from multiplying the computed value oi xhy j — j ^ or 

\ W / /„ a u wl 
log 6^=6:2161. 

By comparing different values of IT, we may compare the 
performance of different powders in the same gun, even when 
fired with different charges, provided the weight of the pro- 
jectile is constant, which is usually the case.* 

THEORY OF COCOA POWDER. 

The facts that, although almost all possible combinations 
of the ingredients of ordinary black powder have at different 
times been tried without decided advantage over those gen- 
erally adopted; and that, as we have seen, the changes in 
manufacture which have had as their object an increase in \i 
have necessarily correspondingly reduced ?/, indicate that the 
difference in the action on the brown powder is due to some 
marked difference in the chemical composition of its charcoal. 

This was for some time a secret for which it is said that the 
British Government paid a large sum. Without requiring 
such payment, the Messrs. Du Pont, of Wilmington, Dela- 
ware, the manufacturers of a powder that has shown itself to 
be nearly equal to that made abroad, have furnished the basis 
of the following theory as to its peculiar behavior. 



* So many of the records require the value of u to be assumed from the 
proportions of the gun, and so doubtful is the accuracy of many of the 
pressures recorded before the theory of the pressure gauge was well 
understood, that the constancy of x ^o"" ^ given gun and powder is best 
seen from an analytical discussion in Chapter XII. The table is given 
rather for illustration tha\. for proqf. 



28 XI. — COMBUSTION IN A GUN. 

The charcoal made by superheated steam contains a large 
proportion of free hydrogen and much more in relatively 
unstable combination. 

The carbo-hydrates^ as are termed the resin, gum and 
sugar added during manufacture, are also magazines of 
hydrogen. 

The effect upon the velocity of combustion, due to the 
presence of the gum and to the high density of the powder, 
and possibly also some of the phenomena of dissociation 
under high pressures, prevent the sudden liberation of the 
hydrogen and its combustion when x^ Eq. (1), is small. 

The hydrogen combines as the pressure wanes, and tends 
to sustain the pressure and to increase both 7\ and //, whereas 
in black powder they must vary inversely. 

The water formed serves to precipitate the smoke, the solid 
particles of which are entangled in a condensed spray of 
liquid gum following the projectile. 

To this may be added, as a theory more generally accepted, 
that the large proportion of nitre tends to prevent the forma- 
tion of CO, thus reducing the volume of the gases first formed, 
and diminishing the violence of their action, or increasing \ji„ 
On the other hand, the excess of nitre may tend to increase 
7\ on account of the more perfect combustion of the charcoal 
and the high calorific value of the hydrogen which it contains. 

The precautions usual in manufacture are taken to affect the 
size, shape and density of the grain and the amount of moist- 
ure it contains, so as to increase its progressiveness. 

That these precautions alone do not account for its peculi- 
arities appears from the fact, that while a prism of black 
powder burns in the open air in \\ seconds, and a similar 
prism of brown powder burns in 10 seconds, equal charges 
of the brown powder give equal or higher muzzle energies 
than the black powder without exceeding their maximum 
pressures. 



XI. — COMBUSTION IN A GUN. 29 

English Experiments of 1890. 

1'hese furnish the following data from which the effects of 
the composition of the powder may be observed. 
SoHd residue per cent : 



Permanent gases per cent of volume : 



7\ oi permanent gases above 
Heat units per kilogramme 
/= v^ H. (Chap. IX, page 7) ratio 
Specific volumes of water vapor 





Black. 


Brown. 


K.CO, 


m 


64 


Kir CO, 


— 


14 


s 


9 


— 


K,S 


15 


— 


KSO, 


10 


22 


iim(3 • 


100 


100 


UIIlC . 

CO, 


47 


51 


CO 


16 


3 


H,S 


3 


— 


ZTand CH^ 


4 


4 


N 


30 


42 




100 


100 




278 


198 




721 


837 


•atio 


1.0 


0.83 




41 


122 



XII. — SARRAU S FORMULAE FOR INTERIOR BALLISTICS. 



CHAPTER XII. 

SARRAU'S FORMULAE FOR INTERIOR 
BALLISTICS. 

The deductions of M. Emil Sarrau permit a very accu- 
rate solution of many important problems affecting the 
interior form and the method of loading cannon. 

By methods which are too elaborate for present instruc- 
tion, Sarrau deduces four general formulae for pressures 
and velocities. 

Notation. 

The units in the following notation are based upon those 
adopted in the publications of the Ordnance Department, 
U. S. A. Some changes are made in the notation to make 
it agree with that previously used in this work. Where 
Sarrau's notation differs, it is given in brackets. 

Let 
V. (v) Muzzle velocity, in feet per second, 
/o (F^ Maximum pressure on bottom of bore in pounds 

per square inch. 
/ {P) Same on base of projectile. 
d. (c) Caliber in inches. 
u. Length of the travel of the base of the projectile in 

the bore, in inches. See Chapter XI, page 13. 
W (/) Weight of projectile in pounds. 
w {n) Same of powder. 
A Density of loading. 

d Specific gravity of the powder. 

N' The granulation of the powder, or the number of 

grains per pound. 



2 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 

/ Force of powder when A = 1, Chapter II, page 7. 

r Time of combustion of a single grain, referred to a 

standard grain as unity. See page 5. 

S Initial volume in cubic inches; the same as F,Chap- 

ter IX, foot page 3. This volume generally 
differs from the capacity of the powder chamber 
since the base of the projectile may occupy some 
of this space. 

8 The reduced length of the initial air space which is 

equal to v' (Chapter IX, page 3) + ^' (Chap- 
ter XI, page 2). 

We have z=S — v. but 

4 ' 

e 27.68 7£/ , 27.68 7£/ ,, . 
o.= and z^,= : therefore 



A 
110.72 w 



(i4) 



a and / (Sarrau uses \ instead of /). 

These are two numerical coefficients depending on 
the form of the grain, which are functions of the 
ratio of the least dimension of the grain to its 
other dimensions. See page 3. 

a and fi. Two very important characteristics depending 
on the nature of the powder; viz, both on its form 
and the time of its combustion. Their values are 
obtained from the following equations : 



m 



^= r (3) 

Owing to their preponderating effect in the prin- 
cipal equations which follow, a is known as the 



XII. — SARRAU'S FORMULif: FOR INTERIOR BALLISTICS. 3 

pressure characteristic^ aod p as the velocity char^ 
acteristic. 
A, B, M, K. Certain empirical constants to be determined 

by experiment. 
Form of Grain. 

If we develop Equation 5, Chapter X, according to the 

ascending powers of — the development may be placed 
under the general form * 

j=/w=<.i(i_/i+«i;+&c. . . . .) (4) 

This may be shown to apply to other forms of grain 

besides the sphere, the coefficients of — varying with the 

form of the grain and by their values characterizing the 
mode of combustion in so far as it is affected by the form 
of grain. 

I. For spherical grains it readily appears that 
a; = 3; /= 1; m = Yi, 
The coefficient m is neglected as insignificant. 

Besides the spherical grain, which includes not only true 
spheres, but grains the form of which approaches that of a 
sphere, such as cubes, hexagonal powders and those of 
irregular granulation ; powders are classified as to form, as 
parallelopipedons and pierced cylinders. Both classes in- 
clude the forms most closely resembling the type, e. g. L. X. 
powder would belong to the former, and pierced prismatic 
powder to the second class. 



* In the above equation replace — by jr, then 
f {t) =z\— {X — x)^ =^^ X — 2, x" ■\- x^ 

= 3-(i — + -') = T [1-7+1(7)'] 

For grains of other forms a similar but more extended method is followed. 



4 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 

II. For the parallelopipedon, if x and j^ represent the ratios 
of the least dimension of the grain to its other two dimensions 

the development of the corresponding function of — will give 

T 

the following characteristic values for the coefficients a and /, 

a 
If the base of the grain be square, x — y^ and 

a=.\-\-%x; I— •• 

a 

III. For the pierced cylinder, x represents the ratio of the 
thickness of the walls of the cylinder to its height, or con- 
versely; the lesser dimension being divided by the greater 
in either case. The cylinder is supposed to burn all over 
at once. The following are the values of the coefficients 
for the pierced cylinder described: 

a=:l-{-xj 1= -. 
a 

Since the ratio x has generally given to it a value of J 
we may form the following table. 



TABLE I. 



Values of ^ 



Form of Grain. a I 

I. Cubical; Spherical; Hexagonal; 

Irregular granulation 3.0 1.0 3.0 

II. Parallelopipedon ; flat powder 2.0 g 3.2 

III. Pierced prism or cylinder, one hole f J 4.5 

By substituting these values of a and / in Eq. (4) we may 

represent graphically, as in figure 1, the variations in the 

rate —=^o for grains of equal weight but of different forms, 
burning in the same time t. 



XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 



If the rate of conversion is uniform, Eq. (4) becomes 

t 
f {t)-=.a- and /, /? and y (post) reduce to 0. 

T 

Size of Grain. 

The mean diameter of irregular grains results from know- 
ing their specific gravity and granulation as follows* 

/6x27.68\i / 52.86 \1 

For powders of regular granulation a similar method may 
be preferred to the actual measurement of their dimensions. 

VELOCITY FORMULA. 
Monomial formula for quick powders 



'=Ma (i) 



Binomial formula for slow powders 



(A) 



in which 



F=Aa(wu)^^-^y[l-rl (B) 

The choice of the formula to be employed in any case 
depends upon the value of y. With a given gun and pro- 
jectile this depends upon the value of /3 and therefore, 
under the conditions of loading, /3 measures the quickness 
of the powder. 

The form of the function y shows that its value depends 
largely upon the gun as well as upon the powder. Conse- 

*Ca\\v=s -—the volume of the mean grain, the weight of which in 
pounds is w : then 

^vze;-i 27.68- '^^vrd^. 



6 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 



qiiently the same powder may be quick in some guns and 
slow in others. Chap. XI., p. 24. 

When y > 0.273, Equation (A), should be employed, and 
conversely for Equation (B). The two equations give but 
little difference in results when the conditions make y 
approach 0.273. 

Referring to the value of /?, Equation (3), it appears 
that the value of y cannot be known until r has been deter- 
mined. It is evident that the methods described in Chapter 
VIII are not sufficiently accurate, so that the following 
practical method is adopted. 
Determination of Constants. 

A well defined molded powder is taken as a standard and 
its values of / and r accepted as unity. For this powder 

the values of a and (i, Equations (2, 3), reduce to y a and /, 
which can be measured by the means described, page 3. 

To determine the value of M in equation (A) we substi- 
tute the value of F obtained as the mean of several fires in 
a gun in which the standard powder is relatively quick, and 
solve with respect to M. 

In equation (B) we proceed similarly for A and B, select- 
ing two very dissimilar guns and taking their conditions of 
loading so as to cover as wide a difference of limits as is likely 
to occur in practice. 

Choice of Formula. 

Inasmuch as the values of A^ B, J/, are true for all 
powders, and since (Chapter IX, page 6) the force of all 
nitrate powders may be taken as constant, and in this case 
equal to unity, equation (A) may be written 



--(0'(v)- 



S 1 ,1 8 



and placing 



M^^^ = X (7) 



Xll. — {JARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 7 



we obtain 

r = «*/-3X«. (8) 

If this value of r substituted in that of y, Equation (6), makes 
'y> 0.273, Equation (A) may be used; but if it makes y< 
0.273, Equation (B) must be employed. 

To determine the true value of t for use in Equation (B) 
requires a method of approximation which .s too long to be 
given here, but can be found in the works mentioned in the 
bibliography. This will not generally be necessary, as the 
characteristics may be determined directly, as hereafter ex- 
plained. 

The value of r for the standard powder is approximately 
equal to the time of its burning in air at the rate of about 
0.4 inch (1 decimeter) per second. Other values of r will 
therefore have approximately their values in air. 

Rejnark. — The first term in liquation (B) represents the 
ideal case in which the form of the grain is such that the 
rate of conversion (Note, foot page 2, Chapter X.,) is uni- 
form. The second term is sub tractive and represents the 
effect of the decrease of the rate of conversion, or of the 
burning surface, when the grains have the forms required in 
practice. It is evidently an advantage to have the second 
term as small as possible. 

Empirical Constants. 

The numerical values of A^ B, M^ the determination of 
which has been incidentally described, depend only upon 
the units of measure adopted for dimensions and masses. 

In the Ordnance Department, the units being respectively 
the inch, for internal dimensions of guns; the foot, for 
velocities per second, and the pound, the constants have 
the following values given by their logarithms : 

log A = 2.56635 ; log ^= 2.80964; log M= 2.84571. 

The other terms in the formula require no change ; since 
the effect of changes in the units by which the different 



8 XII. — SARRAU's FORMULA FOR INTERIOR BALLISTICS. 

elements of loading are measured, is compensated for by the 
numerical value of the empirical constants. 

PRESSURE FORMULA. 

The following equations are employed to determine the 
pressures on the base of the projectile and on the base of 
the bore. 

p=Ka^£u ( Ww)^d-\ (Q 

in which log ^=3.96198. 

/o=^o «' A W^ wU-^, (P) 

in which log ^o=4.25092. 

Equation (C) is obtained by differentiating the equation 
for velocity and determining the maximum acceleration of 
the projectile; it can be verified only by the apparatus 
described Chapter VII. But equation (D) can easily be 
verified by the pressure gauge. See Chapter XI, pp. 8 — 9 

PRESSURE CURVES. 

In designing guns it is indispensable to know something 
about the pressure at other points along the bore than that 
at which the maximum pressure occurs. 

In Chapter IX we have considered an approximate solu- 
tion; but Sarrau's formula furnishes us a method which is 
much more accurate. 
Expansion Curve. 

If in equation (B) we call 

J,=Aaw^\^-jP^j f (9) 

M.=BJ3^^> (10) 

For the same gun, conditions of loading and powder, 
equation (B), becomes by writing, v, the velocity at any 



XII. SARRAU'S FORMUL/E FOR INTERIOR BALLISTICS. 9 

point of the bore, for F, the muzzle velocity, and calling u 
the variable length of travel of the projectile. 

v^A^u\{\-B^u\). (11) 

If we differentiate equation (11) with respect to v and u^ 
and divide by dt^ we have 

^ = (|^,«-|-J/(,^,«-j)^ =/(«)$. (12) 

in which -y- = v and -^ = acceleration of the projectile, or 
at at 

dv i) 7T d^ <"" 

calling/, the variable pressure on the projectile ; —=<-L- ^, 

From this follows 

Combustion Curve. 

It is not recommended to depend upon the values of /, 

u 
thus deduced for a travel of the projectile of less than ^ ; 

because the velocity formula is not considered reliable for 
such small values of u as those existing during the com- 
bustion period. Chapter XI page 1. 

The form of the pressure curve in the initial portion may 
be determined as follows. 

It appears from the following table based upon the analy- 
sis of Sarrau that the displacement of the projectile corre- 
sponding to the maximum pressure, or C/", is equal to 0.6 Zy 
equation (1). This gives us the locus of this pressure and 
equation (C) gives us the intensity. It remains then to find 
the form of the portions of the curve in the neighborhood 
of the point of maximum pressure. This is obtained from 
the following table which gives the proportion of the 
maximum pressure exerted at points near the displacement, 
Uj above. In this table the variable jo represents the ratio 



10 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 



u d"^ y • • 

_, and — v^ values proportional to the acceleration, since 
z dx^ 

X, in this case represents a certain function of /. It has no 

connection with the quantity x, on page 3. 



TABLE II. 



^0 




y^ 




JVo 


d^y. 

dx^ 


0.1 


0.180 


0.6 


0.710 


1.25 


0.651 


.3 


.605 


.7 


.705 


1.50 


.621 


.8 


.665 


.8 


.700 


1.75 


.590 


.4 


.693 


.9 


.692 


2.00 


.563 


.5 


.700 


1.0 


.680 


2.50 


.513 



That is to say that after the projectile has travelled over 
a distance equal to the reduced length of the initial air space, 
the pressure is -||- of the maximum; etc. 

It is supposed that the pressure on the wall adjacent to 
the base of the projectile is to that upon the base, as 10 is 
to 7; so that by multiplying the pressures just determined 
by 1.43 it is easy to determine the probable intensity of 
the corresponding pressure on the walls of the bore. 

QUICKNESS OF POWDER. 

Sarrau has established for powders fired under various 
conditions of loading certain moduli of quickness which 
express their relative quickness under these conditions. 
See page 5. 

The modulus of a powder forms an important independ- 
ent characteristic which is of considerable help in establish- 
ing auxiliary equations of condition for the solution of 
problems in Interior Ballistics. 

It may be shown from equation (B) that if, among the 
variables in the second member, r alone be caused to vary, 
the function, F, will pass through a maximum state. 



XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 11 



In practice this is not absolutely true ; for, as already 
stated in Chapter XI, the smaller the time of combustion, 
the greater the number of volumes of expansion in a given 
gun, and hence the greater the kinetic energy due to a 
given charge. 

Equation (B) is derived by a process of approximation, 
and its physical significance cannot therefore be rigorously 
interpreted. It serves to show, however, that there is a 
limit below which the reduction in r has but a very slight 
effect upon the velocity, and which it is inadvisable to pass; 
because, as r diminishes past a certain point, the velocity 
increases very slowly; but the maximum pressure very 
rapidly. 

The value of r corresponding to the maximum value of 
Fis obtained by placing equal to zero the first differential 
coefficient of the second member of equation (B) regarded 
as a function of r and solving with respect to r.* 

Denoting this value of r which is called the time of the 
maximum (velocity?) by Tj we have 

r. = 3^((^. (14) 

a 

In a given piece a powder behaves as a slow powder 
when the time of its combustion, r, is notably greater than 



* Equation B may be written, 

V=C\p{t)=^CiT-\ — RT-\\ 
in which 

.=.£(i^ c=. (/«)»(.„)» (A); 

Hence 

— =C(— ^r 2-\-\Rt 2) 



by placing —- =0. 

a T 



r,=.S^^SJ^'JKpl 



(U) 



12 XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS. 



that which in the particular arm corresponds to the theoret- 
ical maximum of velocity. Further, two powders fired in 
different pieces should be considered as equivalent as far as 
regards quickness if their times of combustion are propor- 
tional to the times of the maximum for the two pieces 
employed. Consequently we may call the ratio 

^ = ^ (15) 

the modulus of quickness under the particular circumstances 
under which the powder is fired ; since the more nearly does 
Tj equal t, the more nearly does q approach unity.* 

Under this view we may adopt the following arbitrary scale 
for the classification of powders : 





TABLE 


III. 




Value of Modulus. 






Nature of Powder, 


1.0 






Very quick. 


.9 






Quick. 


.8 






Medium. 


.7 






Slow. 


.6 






Very slow. 



Since the above classification was proposed by Sarrau, it has been 
found advisable to extend the value of the modulus in both directions. 
For long Sea Coast guns it now runs as low as 0.4, while it has been 
found advantageous in the B.L. mortars to increase it to 1.3. 

In any case we have 

(W u)^ 
q=^Bp^—^=dy. (16) 

VELOCITY AS A FUNCTION OF THE MODULUS. 

By introducing q in place of r in equation (B) we may 
obtain a new and useful monomial equation of the general 
form 



* The modulus of quickness also is designated by Sarrau as x. 



XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 



13 



V=^A^,B)-^(l{y±^^ (17) 

in which /(^) may be taken as Nq^\ N being some con- 
stant.* See page 28. 

Collecting the different empirical constants under one 
head, which we may call M, and ascertaining that for the 
particular form of / (q) employed we have 

n = i^fZ^.; (18) 

we find that equation (17) reduces to 

In equation (A') V varies with n\ that is, with the 
modulus, ^, upon which by equation (18), n depends. It may 
be used as an approximation, as on page 6, by giving to 7t a 
constant value under conditions of loading which are such 
that the modulus is comprised within certain limits. 



*This equation shows that under given conditions of loading the initial 

//a\\ 
velocity is proportional to I -y I . 

This factor is called the ballistic coefficient. It depends both upon the 
force of the powder and the form of the grain. If the force be considered 
constant, the ballistic coefficient depends only on the form of the grain. 

By transforming Equations ( 2, 3) we have 

^ -T-J' 

It will be observed from Equations (C^), (D^), that the pressure varies 
with the square of the ballistic coefficient. This relation imposes a prac- 
tical limit to increasing the velocity by the increase of this coefficient. 

The ballistic coefficient of the powder must be carefully distinguished 
from the ballistic coefficient of the projectile to be hereafter discussed. 



14 XII. — SARRAU*S FORMUL.*^ FoR tJJtERlOR BALLISTICS. 



It is convenient to remember that n increases as q de- 
creases: when ^=i\-, ^=-J; and when ^=3^, n:=\* 

It is considered that these are the limits imposed by 
practically satisfactory conditions of loading. See page 21. 
By making q—^ equation (A') reduces to the form of 
equation (A), which was thus derived. 

Since q—'6y and since the value of q=^ is taken to be 
about the highest modulus that can be profitably employed, 
we see why the maximum value of y on page 5, has 
been determined =3^-^-3=0.273.* 

MAXIMUM PRESSURE AS A FUNCTION OF THE MODULUS. 

By substituting for - in the value of a', equation (C), its 
value — derived from equation (14), Sarrau finds 

^=^(3^)-^^^(v)^. (C) 

and similarly 

A = ^o(3^r -/-(»^) ^(v) i- («) 

PRINCIPLE OF SIMILITUDE. 

Two guns are similar when all their homologous linear 
dimensions are proportional to their calibers. Chapter 
XVI, page 17. 

The similitude is extended to the loading when the 
weights of the powder and of the projectile are proportional 
to the cube of the calibers, and when the grains of powder 
have the same form, composition, density, etc., and their 



^Although not so named, it is convenient to think of n as the modulus 
of slowness. 



Xlt. — §ARRAU*S FORMULife fOR iNtEklofe 6aLUSTICS. 15 



dimensions are proportional to the calibers. Consequently 
the numerical coefficients a^ /, must have the same values, 
and the value of r must vary proportionately with the caliber. 

The principle of similitude enables the following proposi- 
tion to be proved, viz. : 

In similar gims, similarly loaded^ the velocities and pressures 
corresponding to distances passed over, which^ measured ifi cali- 
bers, are equal, are respectively equal to each other. 

For, let us consider two guns having calibers respectively 

equal to d and to d' such that d' z:^ B d, and substitute in 

d' 
Eq. (16), (17), the ratio d z= — raised to powers varying with 

d 

the quantity considered, as follows : 

From the conditions of similitude we have 

w:w' :: W: w^':: d^ : d'\ 



or 



7e> - W ~ \ d ) —^ ' 



u' d' 
and Ji = 4_ = 6>. 

u d 

In Eq. (17) the factors A, B, A, N, and the ballistic co- 
efficient will be eliminated by division, so that substituting 

for — |- , (03)i = $1 and so on, we have 

I q' r 

Similarly in Eq. (16) since /? =r --, zr — j Q. 



T \ q' 

Now if T varies with the caliber, —j- = —^, and — = 1, 



T ~"6I 



or V= V, 

Since the muzzle may be taken at any distance the propo- 
sition is proved as to velocities and can be shown to be true 
as to pressures by the similar treatment of Equation (C). 



16 XII. — SARRAU'S FORMUL.^ FOR INTERIOR BALLISTICS. 



But if the same powder is used in two similar guns of 

r V d'^ 

different caliber — r- = 1 and -yit- = (QY = -7—. 
t' V d^ 

Consequently, for the same powder in similar guns, the ve- 
locity varies as the ^z**^ power of the caliber. 

Equation (D) similarly shows that when the same powder 
is used in similar guns the pressure varies as the caliber. 

This is a more exact explanation of the practice of vary- 
ing the size of the grain to suit the gun than that given 
Chapter XI, page 7. 



INFLUENCE OF THE CONDITIONS OF LOADING 
UPON VELOCITIES AND PRESSURES. 

General Statement. 

Let us consider as constant for any gun the quantities d^ 
u, IV, and as constant for any powder its force and form of 
grain, or/, a and /, i.e., its ballistic coefficient. 

The quantities which may then be varied so as to affect 
the velocities and pressures are w, A and r. 

There are an infinite number of sets of values of these 
variables which will give the same velocity with different 
maximum pressures, or the same pressure with different 
velocities. The pressures considered are those upon the 
breech of the gun. 

The following practical rules result from differentiating 
the Napierian logarithms of the above named variables in 
Equations (17) and (D'). In equation (17) the differential 
of the Napierian logarithm of the function of ^ which it 



XII. — SARRAU'S FORMULi^: FOR INTERIOR BALLISTICS. 17 



contains can be shown to reduce to the form * 

'^l0ge/(?)=-«^, (19) 

and in equation D', 

d\oz,q= -—-; (80) 



therefore 


d V dw d b. dr 




dpo dw d l\ d t 
po ~^ w "^ A ~r 



(21) 

(22) 

These equations enable us to determine the variations 
in velocity and pressure corresponding to very small incre- 
ments of the variables w, A and r. 

The influence of each variable on the value of the velocity 
and pressure is measured by the coefficient which multiplies 
the relative variation of each variable in the above equations. 

In Equation 21 the coefficients of , , and are 

respectively § ; \\ n = ^ S^T^ ' 



bince a = — ; a^ = == — (/ — 

^ r T T T 

dq dr 

Also d log. f (q) = d loge N q-=J-S^L^ 

A/ q'^ 

d q^ n q^~^ dq 

d T 

=.11 d loge <] = '' 

The increments here discussed are small finite differences made in ad- 
justing practically the conditions of loading. For considerable differences 
Equations (A, B, etc.), should be employed. 



18 XIT. SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 

The third coefficient varies with r and is equal to for 
T i^ Tj. Its value increases with r, but does not exceed ^ 
except when q is less than -^ which is not likely to happen 
in the ordinary conditions of practice. 

Comparing equations (21) and (22) it appears that while 
in equation (21) the variables are arranged in the order of 
their relative importance, in equation (22) the influence of 
w on the maximum pressure is less than that of A or r. 

Let us consider as a fundamental condition that the maxi^ 
mum pressure remains at a constant value determined by the 
strength of the gun, and suppose but two of the quantities 
Wy A and r to vary at a time, the third remaining constant. 

First Case, a and r variable, w constant. 

The equations reduce to 

d t. dt ^ 

-^ = — and (23) 



%'{^y-^ («) 



Therefore, if A is varied by changing the size of the 
chamber for a given charge, the time of burning must 
change correspondingly to the density of loading. In such 
a case, if ^>-5%, T increases with A. Hence the conclu- 
sion: In order to obtain the greatest velocities we should 
use high densities of loading and slow powder. 

Second Case. z£^ and r variable ; A constant. (M. L. gun.) 

Equation (22) becomes | = , (25) 

and equation (21) ^ = f (J - «) ^ , (26) 



* That is, that if we increase w by 10 per cent ; then, to fulfill the fun- 
damental condition, r must be increased ^, or 7.5 per cent. 



XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS. 19 

It follows from equation (18) that since when q is equal 
to 0, « = J ; and that when q is greater than 0, n is less than 
J, the factor (J — n) is always positive and therefore that the 
velocity increases with the charge of powder, and that the 
maximum pressure will not be exceeded provided that the 
time of its combustion be regulated as required by Equation 
(25). 

Third Case, w and r variable in a chamber of constant 
capacity. We have supposed in the preceding cases that 
the volume of the powder chamber can be increased or 
decreased at will, and in designing guns to perform certain 
work the conclusions reached are useful. Suppose however 
that we desire to improve the conditions of loading of an 
existing cannon. In this case, since 



A = 


27.68 w , d t. 

wp nivp 


dw 


(27) 


o A 


and therefore 










dV ,dw dr 




(28) 




dr dw 

r -* w' 




(29) 




dV ... ^dw 




(30) 



in which (^— «) is positive. 

Therefore, if the chamber is large enough, we may in- 
crease the velocity without changing the pressure by using 
a larger charge and a slower powder. 

Examples. 
1. Suppose with a slow powder (;/ = |) we wish to increase 

F by 10 per cent, -^ = j^ .= ^ = ^ ^ ... ^«, = 
53.3 per cent, and = — 53.3 = 93 per cent. That is, we 



20 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 



would use nearly double the charge of double the size of 
grain ; assuming that r is proportional to the size of the grain. 
2. Using a quick powder {fi = g) and 

~V = To = 32" loo •'• ^"^ =" ^^ P"' "'""'' ^"^ ~r -= ^^ 
per cent. Or we would use about one-quarter greater charge 
of less than one-half greater size. 

Fourth Case, w and A variable and r constant. 

This corresponds to the use of the same powder in guns 
having different chambers. 

From the conditions we have 

~ = -i~' (31) 

y=A'^- (3.) 

That is to say; that if we fix the size and shape of the 
grain, and wish to increase the velocity, we must increase 
both the weight of the charge and the volume of the 
chamber. 

General Remark, 

A review of the preceding cases shows that whenever t 
varies, F is a function of n and also of either wov A according 
to which one of these is variable. 

THE EFFECT UPON PRESSURES AND VELOCITIES OF 
VARYING THE TIME OF COMBUSTION. 

If in equation (21) we allow only r to vary, we have 

_=-;._. (33) 

The value of n increases as the modulus decreases; conse- 
quently the same relative variation of the time of combustion 
has a greater influence upon the velocity as the powder be- 
comes slower. See Chapter XI, page 18. 



XII. — SARRAU'S FORMUL/K FoR INTERIOR BALLISTICS. 21 



(34) 



Now, suppose the pressure to vary; under the conditions 
equation (22) reduces to 

dp^ _ _ ^^ . 

Combining this, with equation (33) we obtain the very simple 
relation 

^=.^%. (35) 

V p^ 

which expresses a relation between velocities and pressures 

similar to that between velocities and times of combustion, in 

Equation (33). 

It has been stated page 12, that the values -^ and ^ 
may be considered as the limits that the modulus should not 
pass. The choice of these limits is justified as follows. 
When the modulus is greater than -^ the relative variation 
of the velocity depends upon n in equation (35) which under 
these circumstances only becomes \ of the relative variation 
of the maximum pressure. Consequently, a sensible incre- 
ment of the velocity is obtained only with a considerable 
increase in the pressure and the energy acquired by the pro- 
jectile is imparted at an increased risk to' the gun. This 
grows less as the modulus diminishes from -^^ ; because 
the value of n increases; but then, from Equation (34), the 
relative variation of the velocity corresponding to the same 
relative variation of the time of combustion increases, as 
shown by Equation (33), so that the influence of accidental 
irregularities of the powder upon the velocity continually 
grows greater. 

It is then advisable to fix an inferior limit for the modulus 
so as to preserve uniformity in velocity. 
APPLICATIONS. 

1. To determine the characteristics a and y5 of a powder. 

The most practical method is to use according to circum- 
stances either equations (A) or (B) in connection with equa- 



S^ Xlt.— SARRAu's FORMULA FOk INTERIOR BALLlStlCS. 

tion (D), and to substitute in these equations for V and p^ 
the mean of several measured velocities and pressures ob- 
tained under invariable conditions of loading. 

We have then two independent equations involving but 
two unknown quantities, a and /?; these may then be deter- 
mined without reference to their separate factors. 

By the theory, the characteristics are entirely independent 
of the gun. In this respect, and also in that they give us 
numerically the influence of all the elements of firing, Sarrau's 
formulae are more useful than those, like Noble's, described 
in Chapter XI. 

Having determined accurate values for the characteristics 
of a powder, we may compute the velocity and pressure to 
be expected in any gun whose dimensions are known, when 
the conditions of loading are given; and conversely, the 
dimensions may be determined. 

Within reasonable limits of variation of the quantities 
entering them, the accuracy of the formulae has been abun- 
dantly verified. 

EXAMPLES. 

1. To find the characteristics of Du Font's P. N. (Brown 
Prismatic) powder from a single firing of the 8 inch B. Iv. 
Steel Rifle. For its dimensions see Table IV. 
Data. 2£/=110; fr= 289; A =0.980 ; z/= 1878; /„= 36000; 
^/ = 195.75. Equation (D) gives us 

«2= i^ — - =0.9706=log-il.98704. 

An application of the test mentioned page 6, will show 
that the binomial form.ula is applicable; although this might 
be assumed for powders of this kind. If then we write 
equation (B) so as to combine in each term the quantities 
relating to the gun and the conditions of loading, we may 
reduce it to the form 



XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 23 



XF=a-a(3V or jS^"""^^, 

a V 
in which Fis measured and 

— = — > (- /v and Y= — ^^ -. 

Substituting in the above the known values of a, X, V 

and K we find 

log i3 = 1.33725. 

Another method is to fire the same powder under very 
dissimilar sets of conditions in which W^ w, u, d shall have 
different values and to determine the values of V under 
these conditions. 

We may thus obtain two formulae of the form of the above 
value of XV; as these involve but two unknown quantities, 
the characteristics sought may be determined. 

This method avoids all uncertainty attending the oper- 
ation of the pressure gauge; but the former method is gener- 
ally preferred as the conditions more nearly resemble those 
of practice, and introduce the customary unit of measure- 
ment of pressure, 

2. To compute the muzzle velocity to be expected from 
the 8 inch B. L. Steel Rifle for the preceding powder. 
Data. 7i/=105; A =0.935; /^=289. 



Computati( 
log B = 
log^ = 
log W\ = 
log u^ = 
log d-' = 


)n of y, 

2.30964 
1.33725 
1.23046 
1.14585 
1.09691 


Computatic 
log^ = 

log a = 
log wt = 
log A^ = 
log u^ = 
log IV-^ = 
log d-^ = 
log(l-;K) = 
log F = 
V = 


m of V. 
2.56635 

1.98704 
0.75795 
1.99276 
0.85939 


log y 

y = 

l-y= 


1.12011 
0.13186 
0.86814 


1.38477 
1.77423 
1.93859 




3.26108 
1824.3 



24 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 

By actual measurement Fwas found to be 1825. 

3. To compute the maximum pressure on the breech 
under the same conditions as in No. 2. But with a powder 
{PO) of which the characteristics are different, viz.: — 
a=log-il.97701; y5=log-il.28978. 



log^o 


= 


4.25092 


log a* 


= 


1.95401 


log A 


= 


1.97102 


log w^ 


= 


1.51589 


log Wi 


= 


0.61523 


log ^-2 


: 


2.19382 


log A 


4.50089 


A 


= 


31688 



From actual firing under the above conditions the mean 
value of A as determined by two independent pressure 
gauges was 31700 lbs. 

4. In order to avoid injury to valuable cannon, it is custom- 
ary at the Proving Ground to make a preliminary trial of 
new powders in what is called the proof gun. 
Data. w=35.9; «^=181; A =0.8988; ^=8; A=20420. 
Find the value of A to be expected when 

ze/=90; «^=300; A =0.8018; ^=8. 
The first set of data give in Equation (D), 
log a2:=0.18085, 
hence, we find for the second set of data, 
A=41174 lbs. 
In actual firing the mean value was found to be 41055 lbs. 

Useful Tables. 

The following tables give the dimensions of various cannon 
of the U. S. land service with the characteristics of different 
powders tried in them and the resulting pressures and 
velocities both computed and as verified by measurement. 



XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 25 

They will be useful in solving problems hereafter. 
Table IV. 



Pow- 
der. 


Gun. 


d 
inches. 


u 

inches. 


W 

lbs. 


w 
lbs. 


A 


V 

feet per 
sec. 


11 ^'' 
lbs. per 

eq. in. 


LX... 


3'^20B. L. rifle.. 


3.2 


73.2 


13 


3.50 


0.857 


1,649 


31,000 


LXB. 


....do 


3.2 


73.2 


13 


3.75 


0.827 


1,756 


35,150 


IKD.. 


....do 


3.2 


73.2 


13 


3.50 


0.857 


1,680 


29,100 


1KB.. 


....do 


3.2 


73.2 


13 


3.50 


0.857 


1,663 


30, £^00 


KHC. 


12^^ mortar 


[2.0 


91.6 


610 


50.0 


0.821 


932 


22,000 


MW.. 


....do 


12.0 


91.6 


610 


48.0 


788 


959 


26,250 


EVF. 


S^^B.L. R Conv.. 


8.0 


98.5 


183 


45.0 


0.792 


1,488 


32,650 


PiV... 


8'^B.L. R. S 


8.0 


195.75 


289 


110.0 


0.980 


1,878 


36,000 


NM.. 


12'^B.L.R.C.L.. 


12.0 


273.5 


800 


265.0 


0.827 


1,688 


26,350 


NV3.. 


....do 


12.0 


273.5 


800 


265.0 


0.827 


1,718 


26,890 


NR... 


....do 


12.0 


273.5 


800 


265.0 


0.827 


1,826 


32,990 


NVi.. 


....do 


12.0 


273.5 


800 


265.0 


0.827 


1,760 


26,625 


NVa.. 


...do 


12.0 


273.5 


800 


265.0 


0.827 


1,756 


28,000 


IB... 


3^M7 M L.R.W.I. 


8.175 


74.6 


10.5 


5.469 


0.814 


1,983 


25,000 


OB... 


12^^ mortar 


12.0 


91.6 


610 


52.0 


0.854 


987 


25,250 


oc... 


....do 


12.0 


91.6 


610 


52.0 


0.854 


942 


19,750 



26 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 







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CO CO 


CO CO 


CC 


00 


CO 


CO 


1—1 


tH 


T-l 


tH 


r-i 


1— 1 




o 


o 


















o 


8 


o 


O 


O 


^ 






a 


(7-t 




























I* 


« 


i:- 


1> 


















lO 


lO 


lO 


lO 


lO 


JO 


1 




O 


o 


















o 


o 


o 


o 


o 


o 


;h 


CD 


fO 


lO lO 


00 lO 


IC 


o 


lO 


o 


CO 


CO 


Tfl 


o 


on 


CO 


C 


ba 


r-> 


<-> 


(jcj (j;j 


c< 


t- 


Cv 


lO 


OJ 


lO 


CO 


CO 


tH 


CO 


tH 


CJ 


r<: 




t- 


r- 


{V. {>■ 


t- tr- 


<^ 


t- 


f^ 


f^ 


00 


00 


00 


Cf) 


on 


00 


^ 


TJl 


tH 


tH 


T- 


J tH 




tH 




T-l 


T-1 


r-! 


tH 


r-t 




■1-1 


1-t 


T-i 


























r^^M 


T^lN 


WOJ 


^^ 


,H|OJ 


w|9l 


> 




O 


o 


o o 


ee 


CO 


CC 


CO 


o 


(>* 


tH 




tH 


1—1 






^ 


r- 


r- 


o o 


Cv 


0> 


o 


O) 


f- 


r- 


tH 


tH 


tH 


tH 




tH 


^ 


Cd 


Ol 


Ci CQ 




tH 




■I— 1 


















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<N c^ 




























»o 


lO 


















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lO 


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T— ( 


r-l 


















t- 


f- 


r- 


f^ 


f^ 


t- 


«» 


CO 


CO 


















"^ 


XJH 


-* 


^ 


-* 


^ 






o 


o 


















o 


o 


o 


o 


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o 






I 




















-^ 


'. 














d 


. 





















o 


I 














ba 






1 






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I 
• 


1 








H 


: 














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(D 


o 


o 


o 


O 


? 


n O 


o 


o 




o 


o 


o 


o 


o 




f;^ 


Id 


^d 


<B 


^ 


03 


^ -T^ 


'd 


'd 


■n 


-d 


^d 


tj 


'd 




fe 


5S 




§ 

e 






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S 




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bo 



XII. — SARRAU'S FORMULiE FOR INTERIOR BALLISTICS. 27 






: w 

: t^ 



CO 

to 

^? 

w: 

< • 
3.: 

o • 



o o 



CLP 



1-^ 00 
to i.. 

o ; 



5^ to 



O 






o p Po go p 9jO 



pj Fl CL p. M &. p. <j 



o? 



or- 



p- p. ^ p^ § 

<3 . CO 



Kind of 
powder, 



CO CO CC p3 po pO CO p3 p5 CO CO 00 to to to 00 00 to to to to to 
I_L 'h-i J-j. i.o to to to to to to to to 
^^ -:i CTi 
Or Oi Or 



I-* to 
rfi. >f>. rf^ CO CO Ci CO CO CO CO CO OI M- Hi M- 00 00 _M- M- h-i CO CO 

OS OS OS to to OS to to to to "to OS OS OS bi bi b> os bs tf^^ br 



V-iOSOSOSM-r-i-OSOSOSOS-qf 
HJLM-(-J.M-l-iM.|-i-l-i|-'->-i-l-i-G0l-il-^i-i.QD00l-i.|-i-l-J.<X>Ol 

pp pcocooococooicocooooococcooocoo 
bx QT br "^ 



^ 



^3 



l-i to 

COC^OTOTCT*»-Hf^rf^tO^OS 
Or CT Ol (» pO CO CO CO p3 CO CO Ol to O to O Ol 00 Ql OS CI Ol 

bo bs ht»" ox *-^ o "-3 bi br bi bi 

I-*- to OS CTl OI 
CO or CO 



9°OOQOGOOO?DOOGOOOOOOOi:OQOQOOOOO-:i~3<It^«r>00 

o CO H-^ c;! to o to oi oi oi c;i oi to oi -^ «d oc co to to to 

en ^ j^i. ,<j ^ CO -^ -3 <} •<} -3 rfi. >-»■ rfi^ to to GO CO -3 CD -q 

-*- * 



--^ 



OcDi:o-^-3Ciososcno5Cscoi:Di:o?ociTh4i«'«0«oosrfi-^ 

OOSCOtOCrfM-COOSCOOCOOSOlCO^GOGOOTH-iQTOSOS 
00-3COOSOSOtOCOOCOOOOCOtOOCnOO'<l«DtOOl-»- 



to M'M-h-lM-hJ^M.M.H'M-M.H*. J^^ ^^^ ^ 

o'«o"co'^''-3'bT"^7 Oibl or OS CO «0 CD CD OtV CD CD Os''>j^ -;^ ^ 
f-LOSCOM-C^OOOSlOCOCOGOCDCOQOOOOOajtOOt^OS • 
OOOlCOCCOSI-»tOCOCDCOOOOCOtOOh-iOOCOOlM-OH-i 






lcotocococoto^oo^tototococototo toto 

• or GO O O O CDCO)-^COtOCOOOtOOSCOOO»4^CO 



t0t-^O<{OO00O-QC»O0Srf^OC0OOO'<lG0fJ^M- 






CAStotococototococotoiocotototococototo toco 

OCS 4^ OS Ot -3 cop opp Hi Or H-^ CTf CCJ^sp^jfi-jCi CO tS 
O Vj Ot"bT"H-i"--3'*'<}bfl'^ o'h^'m- O^lOCOOStO^CTtOOO 
OOiOOOtO— ■JCOOOOOOOlOtOCTCJOlOOO 

oooooooooooooooc;toooooo 






WfcStOOOOOC^tOCCM'COWOtOl-itOtOOTI-'t-AOOHiW 



j Kumber of rounds 
considered. 



28 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 



DISCUSSION OF THE COEFFICIENT X^ 

If in Equation (10), Chapter XI, we replace r^ by we 

4 

have after reduction, r =. Tc^rr, — rr ji •> 

in which u is expressed in feet. But since internal meas- 
ures are given in inches we may avoid errors in practice by 
writing this 

12 



in which G = nctAi\ 2 • 
2240 g^ n 

If in Equations (17) and (D^) we replace the ballistic co- 
efficient by C, and collect the constants in both equations 
so that 



3 (3 ^)W 3 ^ ' 

these equations will read 

_^ ^C wl A^' d^ td N q"" ,^„. 

^ =" ^ w^ • ^ ^ 

^°==-^ Wi did ' (^^) 

Substituting these values in Equation (36) we have 

X=Za N^ q^--^ (-^y (39) 

in which Z = ^-^ = log-^ 0.7394, viz., 5.488. 

The factor N, which in Equation (17) was taken as con- 
stant, is not absolutely so.* Its value is given in Sarrau as 

/(,)=iV," = Z^i^>. (40) 

By substituting the value of N impHed in Equation (40) in 

q rt 

♦ For values of f between yp and -^ ,iV"varies only from 1.012 to 1.056. 



XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 29 

the factor N* /""' in Equation (89) and calling the result- 
ing value Q, we have 

This reduces Equation (39) to ^ 

^ = ^^'e(-|^)*. (42) 

Discussion of the Factors of X. 

Of the four factors producing %'. Z is a constant ; C 
depends solely upon the powder; that is upon its force and 
the form of the grain ; Q depends upon the suitability to 
the gun and projectile of the kind of powder employed ; 

— j depends solely upon the circumstances of the particu- 
lar fire considered. Hence, to compare the intrinsic proper- 
ties of different powders fired in the same gun, we may 
compare their respective values of 

The relation between ^ and ^ is shown in figure 2, from 
which it appears that while Q is sometimes an increasing and 
sometimes a decreasing function of q ; for values of q be^ 
tween fj^ and -j^, ^decreases slowly from its maximum value 
of 1.245, corresponding to ^ = ^q, to a value of 1.159, 
corresponding to ^ = -^j* 

If the force of all nitrate powders were truly constant, 

C = —- = -jj- would depend for its value solely upon the 

form of the grain ; and, since within ordinary limits Q does 
not vary greatly, we would expect nearly equally good re- 

* From this we may conclude that for ordinary approximation the mean 
of these values, or ^ = 1.2 may be used. Also that it is not well to 
depart much from the inferior limit of g established by Sarrau. 



30 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 



suits from black or brown prismatic powder. But, in the 
following illustration, taken from one of the best black pris- 
matic powders recently tried, we find /to be so small that C 
does not much exceed the value oP 3.0 deduced from 
Table I, for ordinary powders of irregular granulation. 

We may therefore conclude that the advantage of cocoa 
powder consists in its maintaining its force at nearly unity* 
without becoming so quick (or slow ; figure 2) as to cause its 
value of Q to become unduly small. These considerations 
indicate in a general way that its peculiar properties are due 
to the nature of the fuel it contains. 

Illustrations. 

The following data, derived from experimental records, 
illustrate the principles discussed : 

COMPARISON OF POWDERS. 

Gun Sin. B.L.R. 8in.B.L.R. 

Powder, kind Bl. prism. Br. prism. 

Powder, name O. I. N. Ger. cocoa. 

W. 45.0 289.0 

Sph. Density 2.9 4.5 

V, 1852 1875 

A 33075 35900 

u 119.8 195.75 

a 1.5 1.5 

/ 1 ^ 

* ^ 3 

a" 2.45 0.93 

(i 0.78 0.21 

/. 0.70 0.96 

r 0.43 1.59 

C 3.16 4.45 

q 0.70 0.38 

* See Table V, in which the last six powders are cocoa* 



Xli. — gARRAU*S FORMUL.fi FOR INTERIOR feALLtSTICS. SI 



Q 1.23 1.12 

X observed 28.28 34.32 

X Equation (40) 28.44 34.87 

n 21.26 27.39 

Ratio of n 1.00 1.29 

If we exchange powders only, we have — 

Powder Ger. cocoa. O. I. N. 

q 0.19 1.47 

Q 0.73 0.50 

II 17.95 8.55 

Ratio of n 2.10 1.00 

That is, that while each powder is best suited to the gun in 
which it is actually used, the cocoa powder would be better 
for general use, and might profitably be adapted to the siege 
rifle by reducing the size of the prism so as to diminish r and 
increase Q. 

MAXIMUM VALUE OF X, 

The value of 11 before deduced, enables us to solve some 
very important problems in internal ballistics. 

As an example, let us consider the question of how, with 
our present knowledge of gunpowder, we may attain the 
maximum value of X' Also, let us apply this to a gun the 
construction of which limits p^ ; the spherical density of the 
projectile being known and the value of ?/ being expressed 

8 IV 
in terms of the caliber or // rr n d, Let s = — -— be the 

spherical density of the projectile.^ The maximum value 
of C^ being 4.5, figure 2 shows that the maximum value of 
IT, and hence of x^ will require ^ = 0.6. 

The maximum value of tj will depend on that of A. The 

* See Chapter XVI, page 6. 



82 Xn. — SARRAU*S FORMULi^ FOR INTERIOR SAlLISTICS. 

specific gravity of some powders is now such that a value of 
A =: 1, has been reached. We may consider this a maxi- 
mum, as it is rarely exceeded. After deducing general equa- 
tions, we will apply them to a typical gun based on the 8-in. 
B. L. R. Steel, in which j =z= 4.5 ; ^/ = 24, and take the 
maximum value for /„ as 36000 lbs. per square inch, that 
being what the records indicate to be a desirable limit. 

1. Proper Weight of Charge. 

By substituting the values assigned for JV, A, d, t^, q in 
Equation (D'), it leads to the following ratio : 

^=[log"'n.lll9^']S (44) 

In which, by substituting the special typical values assumed 
for /(J, n and i", we have w = 0.2 W. 

In the 8-in. rifle this would reduce the charge of powder 
about one-half. 

2. Proper Size of Grain. 

If in Equation (16) we place q =s 0.6 and assign values as 
above, we have for a general equation, since / = J 

r = log " ^2.0799 (^s n)h d. (45) 

This shows that, as before stated, the size of the grain 
should, in similar guns, vary directly with the caliber. For 
the 8-in. rifle, this makes % = 1.0, or, from the preceding table, 
the size of the grain should be about 68 fo of its present linear 
dimensions; the force of the powder being unity, and the 
form remaining unchanged. 

3. Maximum velocity. 

The maximum value of H = 5.488 X 4.5 X 1.245 = 30.73. 

But U = X \ wA = x-:7a 3- = 30.73. 

By substituting the value of wl deduced from Equation (44) 



XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 33 

and reducing, we have* 

V= Tlog-^ 2.7355 ^^ ]' ' (46) 

Which in the type-gun gives 

F= 1716, or ;^=: 46.48. 
The largest value of % Y^^ attained with this gun is about 
35.0 ; showing an efficiency of about 80 per cent. 

Remark. 

For sea coast guns, in which the bulk and weight of the 
charge is of no special consequence, since the guns are sta- 
tionary and magazine room is ample ; the waste of the powder 
and the increased volume of the chamber necessitated by the 
present use of very large charges may be neglected in favor 
of the high muzzle energies required. But as the caliber of 
the gun decreases, and its mobility increases, the necessity for 
reducing the weight of the charge becomes more important. 
This is especially true in the loading of magazine small arms, 
the efficiency of which requires the weight of the ammuni- 
tion to be reduced to a minimum ; so that the number of cart- 
ridges that the soldier may carry will be as great as possible. 

* This is independent of the caliber as would be expected from the 
principle of similitude, x may also be shown to be independent of the 
caliber, by substituting values of W and w in terms of s, and of « in 
terms of d. 



XIII. — HISTORY OF GUNPOWDER. 



CHAPTER XIII. 

HISTORY OF GUNPOWDER. 

Origin. 

Knowledge of the properties of nitre as a supporter of 
combustion are attributed to the accidental kindling of the 
embers of a camp fire by the salt, often, in India, found effer- 
escent upon the surface of the ground. As sulphur is not 
essential, its first employment cannot be conjectured. For 
its binding properties honey was used at an early date. 
Early Use. 

The use of gunpowder was at first confined to fireworks 
and rockets. These are mentioned in Chinese records over 
2000 years old, and seem to be indicated in the account of 
Alexander's invasion of India at about the same epoch. 

The transition from its use in a paper tube, or bamboo 
cane, to cannon of different sizes is indicated by the etymology 
of the latter name. The barrel of any fire arm is in French 
called canon. 
Early Cannon. 

The first use of gunpowder as an agent for propelling pro- 
jectiles is assigned to the Moors at the siege of Baza in Spain, 
about 1325; twenty-one years before the battle of Crecy. 
This is about the time that the chemist monk, Berthold 
Schwartz, of Freiburg, is said to have discovered its pow- 
ers by the accidental ignition of a ternary mixture, lying in 
a mortar and covered with a stone. 

Owing to the weakness of the early cannon — which were 
constructed after the manner of ordinary barrels, sometimes 



XIII.— HISTORY OF GTJNPOWDER. 



of iron bars welded together longitudinally and hooped with 
iron tires, and sometimes even of wood, wrapped with 
rope — efforts at first were directed to reducing the strength 
of the new agent. 

Early Powder. 

Therefore, although the best proportions had long been 
known, it was often composed of equal parts of the three 
ingredients, and sometimes mixed with saw-dust, resin, sand, 
or ashes. 

It was often mixed and ground by hand as required, and 
was used in the form of a fine meal or powder^ from which 
its name is derived. 

The diminished velocity of inflammation resulting from 
the use of meal powder favored the end in view; but, since 
the cartridge was yet unknown, the condition of this powder 
made it so inconvenient to load the long guns then used 
that the efficiency of artillery was much impaired. 

Early Breech-loaders. 

To overcome this difficulty in loading, cannon at a very 
early date were made to load through the breech. But the 
arts at that time afforded no means of preventing the escape 
of gas through the joint so formed, and such cannon are 
comparatively rare. 

It will be seen hereafter that the practical utilization of 
this principle depended upon the discovery of the self-sealing 
gas cheeky the best form of which exists in the metallic 
cartridge case, now used for small arms. 

But for this essential improvement m^any of the systems 
now In vogue are but repetitions of these ancient forms, not 
only in principle, but in many details of construction aad 
operation. 

The reciprocal evolution of the gun and its ammunition 
is a striking illustration of the law of continuity. 



Xllf. — mSTORV OF rttlKfOWDER. 



Men have probably always been equally ingenious in util- 
izing the accumulated capital of knowledge at their com- 
mand; but the successful application of even simple princi- 
ples requires, in many cases, the parallel development of 
apparently unrelatec arts. 

Intermediate Stage. 

It was not until near the close of the 16th century that 
cannon, first of copper or its alloys, and then of cast iron, 
were made strong enough to resist the pressures due to the 
use of the grained powder, the use of which had hitherto 
been confined to muskets. This was called corned powder, 
vide pepper-corn J barley-cornj coming-mill. 

Until about the middle of the present century no great 
improvement*: occurred in gunpowder or in cannon. The 
reasons for this were the general assumption that gun- 
powder was instantaneously converted into gas, and the want 
of any apparatus for measuring pressures. 

Use of Eprouvette. 

Gunpowder was proved by firing it from the Eprouvette, a 
small mortar with its axis carefully fixed at an elevation of 
45*. The quality of the gunpowder was determined by the 
distance to which an accurately fitting ball of a given weight 
was thrown by a given weight of powder. Although some 
difference existed in the size of the grain used in different 
juns, the proof 7'ange increased as the size of the grain dimin- 
ished; so that for large guns the size of the grain, as meas- 
ured by our present standard, was exceedingly small. See 
Chap. XI. 

Rodman's improvements. 

1. Pressure Gauge. 

The late General Rodman, of the United States Ordnance 
Department, was the first to investigate the properties of 
gunpowder in the modern method. 



3tm.— tttStOkV Of 6tlNl>6Wt)£R. 



His experiments, conducted with the view of increasing 
the effectiveness of the system of cannon which bears his 
name, depended primarily upon his employment of the pres- 
sure gauge. This was a pyramidal indenting tool, previously 
used by him to test the relative hardness of cannon metals, 
and applied in the manner indicated for the crusher gauge. 

Although open to many grave objections of detail, this 
instrument gave useful relative results and served to draw 
attention to the very erroneous estimates previously made as 
to the pressure exerted by gunpowder. When fired in its 
own volume, this had been variously estimated at from 0.7 
to 700 tons per square inch. 

2. Powder. 

a. Mammoth. 

Rodman's first step was to recommend the use of large 
charges of "mammoth " powder, which was of about three 
times the diameter of the largest powder previously used. 

This gave satisfactory velocities and moderate pressures; 
and, since its manufacture required less granulation than 
before, it was cheaper, pound for pound. 

b. Perforated. 

About 1860, he improved upon this idea by suggesting 
the use of perforated powder, made for small cannon in 
cylindrical cakes, and for larger cannon in hexagonal 
prisms which could be built up into cartridges. 

Owing to the great cost and novelty of this powder, and 
to the intervention of the civil war, the perforated powder 
was used in this country only for experiments ; but the 
mammoth powder has until lately been exclusively used for 
heavy guns. 

DERIVATIVES FROM RODMAN's POWDER. 

Russian Powder. 

The perforated prisms were experimented with in Russia, 
from 1860-1865, being finally made much smaller than 



btllt. — kistORY OF GUNPOWDEfe. 



Rodman's, and pierced with seven small holes. The powder 
was so made in order to adapt it to the muzzle loading guns 
then used. See Fig. IB, Chap. IV. This is known as 
/Russian prismatic powder. 
English Powders. 

The English objected to this powder, saying that, owing 
to the number of perforations it contained and to its dimin- 
ished density, it was liable to break up in the gun. 

About 1875, they returned to General Rodman's original 
idea, adopting the cubical Pebble powder, the cubes, for 
the largest gun , being about lYz inches on the edge. 
United States Powders. 

In the United States, the mammoth powder was im- 
proved upon by the adoption about 1873 of the Du Pont 
Hexagonal powder. Fig. 12, Chap. IV. 

This and the Sphero-Hexagonal powder, Fig. 12, have 
the advantage of great uniformity in the size and shape of 
the grains and in the form of the interstices between the 
grains. They are also progressive, owing to the diminished 
density of the interior of each grain. 

This results from the fact that the effect of compression 
is not transmitted homogeneously throughout the mass 
compressed. The density is always greatest next to the 
moving surface. 

For reasons given in the text. Flat powders of the Z. X. 
type. Fig. 12, are also occasionally used. 
Italian Powder. 

The Fossano powder, made in Italy, consists of an 
agglomeration of dense grains of medium size, set in a 
mass of powder meal and pressed to a density less than 
that of the individual grains. Its operation is distinctly 
progressive. 

The principle is applied to other powders, both molded 
and of irregular granulation. 



Xin. — HISTORY OF GUNroWDER 



MODERN POWDERS. 

In order to obtain the most effective combination of gun 
and powder, each type of gun now requires a special 
powder, and some cannon, as mortars, require more than 
one powder for each mortar. This increases greatly the 
difficulty of supply. 

The kind of powder best suited to each type of gun is 
still (in 1888) undergoing experimental investigation. 

The advantage of adapting the size of the grain to the 
size of the gun, upon which for simplicity so much stress 
has been laid, is becoming of diminished importance, since 
the effects due to increased size may be attained in many 
other ways. 

Owing to the great number of conditions which require 
to be simultaneously satisfied, including the effect of 
meteorological conditions prevailing during manufacture, 
the powder makers find it difficult to meet the increasing 
exactness of the demands made upon them. This applies 
even to the duplication of satisfactory samples. 

Present Custom. 

All large guns of the present day use hexagonal prisms 
like the Russian prismatic, but pierced with a single hole. 
This is easier to make and its ballistic properties are better. 

It is preferably a concrete powder made by consolidating 
under pressure small grains of powder previously com- 
pressed in the ordinary manner. Mealed powder is some- 
times used instead of that which has been grained. 



XIV. HIGH EXPLOSIVES. 



CHAPTER XIV. 

HIGH EXPLOSIVES. 
Classification. 

Except the chlorate mixtures, the high explosives used in 
warfare are all organic nitro-substitution compounds, gener- 
ally of the third order, in which 3 atoms of H are replaced 
by 3 molecules of NOg. 

The most important are Gun-cotton, Nitro-glycerine, 
and their derivatives. The derivatives of picric acid are 
growing in importance, and so, for special purposes, are the 
mono-, di-, and tri-nitro-benzines and naphthalines. 

Those which in their operation resemble the mercuric 
fulminate are C2i\\t6. fulminating compounds, and include, be- 
sides their typical salt, the mixtures in which the chlorates 
are used dry. 

The demands of civil engineering and the hope of success- 
fully adapting these explosives to warfare are constantly in- 
creasing the number of those for which both safety and 
efficiency are claimed. On the other hand, many, once 
famous, are obsolete, so that the following discussion will 
relate only to those of which long experience has demon- 
strated the essential properties, and to the most distinguished 
of recent competitors for the selection of the engineer, 
Danger. 

Although their composition and violence render the hand- 
ling of many as compared with gunpowder, dangerous; yet, 
a knowledge of their properties is demanded b- the con- 
ditions of the time; and, as with gunpowder and steam, this 
knowledge comes principally by experience. 



XIV. — HIGH EXPLOSIVES. 



The disasters reported with such apparent frequency are 
the price of progress toward safety, and point rather to the 
enormous consumption of these explosives, often by ignorant 
and reckless persons, than to any necessary peril when proper 
precautions are observed. 
Commercial Importance. 

The scale on which these explosives are employed, prob- 
ably, as with gunpowder, much greater in time of peace 
than in war, appears from the size of blasts fired almost daily 
in the Californian mines during the period of their greatest 
activity. These blasts often contained 50,000 pounds 
apiece. 

The great blast at Hell Gate, New York Harbor, in 1885, 
contained but six times as much. 

The economic value of an explosive depends so much upon 
the net cost of the work performed that it is interesting to 
note the following relative scale of prices per pound in 1888. 



Explosive, 


Price. 


Proportion. 


Gunpowder, 


20 eta. 


1.0 


Dynamite, 


50 


2.5 


Nitro-glycerine, 


80 


4.0 


Gun-cotton, 


1.00 


5.0 



COMMON PROPERTIES OF GUN-COTTON, NITRO- 
GLYCERINE, AND THEIR DERIVATIVES.* 

Sensitiveness. 

When not freed from the acids used in their manufacture, 
these explosives are prone to spontaneous decomposition 
and tend to form products of a lower order of substitution. 

While undergoing decomposition, their sensitiveness is in- 
creased, but their efficiency when exploded is diminished. 

When properly prepared, they are not sensitive to moderate 



* Cadets are advised to review the articles in the Chemistry which 
treat of nitro-glycerine and gun-cotton. 



XIV. — HIGH EXPLOSIVES. 



shock; but friction, the impact of a projectile, or the shock 

of discharge may cause their explosion. 

Firing. 

As a rule, they all explode at about 200°. When ignited 
by a flame and unconfined, they burn more or less quietly. 
If confined, their explosion is of a low order unless they are 
detonated. Their behavior in this respect depends much 
upon their mass and the resistance of the envelope. See 
Chap. II. 

They possess the remarkable property of exploding vio- 
lently when gradually heated to about 200°; whereas, if 
'dropped upon a red hot iron, they may simply deflagrate. 
Detonation, 

Owing to the variety of the means by which the mercuric 
fulminate may be ignited and to the nature of its product, 
it is almost exclusively employed for detonation, preferably 
alone and pure, and sometimes with a primer of dry gun- 
cotton. 

The detonators are commercially known as blasting caps^ 
exploders^ or fuzes of various degrees of "force " according 
to the quantity of fulminate they contain. The fulminate 
lies in a thin copper tube, one end of which is closed, and is 
ignited either by a quick-match or by the heating of a fine 
platinum wire by the electric current. The detonator is 
placed in immediate contact with the charge, but should be 
so disposed that, if the quick-match is used, the charge shall 
not be prematurely ignited. 

The mass of the fulminate should bear a certain ratio to 
the mass and condition of the explosive; this may neutralize 
the advantages on the score of safety which the sluggishness 
of the explosive confers. 

Long charges may require to have dispersed through them 
several detonators in order to maintain the energy of the 
explosive wave. 



XIV. — HIGH EXPLOSIVES. 



Products. 

Except Nitro-glycerine all the substitution compounds 
yield a large amount of CO, and hence, where potential is 
sought, require the addition of an oxydizing agent. 

Pressures. 

The ordinary gauge being unsuited to measuring the high 
pressures of detonation, special devices have been contrived. 

General Abbott of the U. S. Engineers, in a series of 
experiments (which bear to the high explosives the same 
relation as do Noble and Abel's experiments to gunpowder), 
suspended in water his gauges at definite distances from 
the submerged explosive. 

For experiments in air, charges of given weights are 
detonated either within or upon similar blocks of lead and 
the resulting deformations compared. Or the exact charges 
required to burst similar hollow projectiles may be deter- 
mined. 

Effects. 

General Abbott's experiments give the following scale by 
which to measure the force^ Chap. II, of explosives. His 
results apply only to sub-aqueous mining and indicate the 
paradoxical fact that Dynamite is more powerful than 
Nitro-glycerine. 

He found that the pressures registered by a crusher gauge 
varied as the Yi power of the charge and inversely as the 
1.4 power of the distance. Or calling / the pressure, %v the 
weight of the charge, d the distance, and k a constant vary- 
ing for each explosive and for the nadir angle under 
water. 



3 // kw\* 



These comparative results are expressed by the following 
table: 



XIV.— HtGtt EXPLOSIVES. 



Nitro-glycerine, 81 0.93 

Gun-cotton, 87 1.00 

Dynamite, 100 1.15 

• Explosive Gelatine, 117 1.35 

a result quite different from that of Chap. II. 

On the other hand, extended practice in mining operations 
under ground confirms the relative useful values of the high 
explosives as determined by their potentials and stated in 
Chap. II. 

Three spheres surround the center of the explosion: 

1. The sphere of pulverization. 

2. The sphere of rupture or dislocation. 

3. The sphere of fracture or fissure. 

The relative dimensions of these spheres vary with the 
force and potential of the explosive. 
Tamping. 

The great rapidity of the reaction renders special tamping 
unnecessary, since the pressure of the atmosphere suffices to 
produce many of the effects desired. This is the origin of 
the common idea that such explosives act downward. This 
property is particularly valuable in military operations where 
time is precious. 

The best results, however, are found when they are 
tamped. Even a thin layer of earth or water greatly in- 
creases their effect. For a similar reason the mass of the 
charge is best placed between the detonator and the object 
to be destroyed. 

Example. 

Long iron tubes filled with dynamite have been detonated 
in air without converting all of their contents. When the 
tubes were submerged, the entire charge was detonated, 
Chap. II, page 5. The accidental explosion of charges which 
have been imperfectly detonated leads frequently to disaster, 
and so, it may be said, does tamping with an iron bar. 



XIV.— tttGli eX!>L6S1VES. 



Physical Condition. 

The greater the density of the explosive the smaller the 
bore hole required to receive it, and hence the greater its 
economy. 

Plastic explosives are valuable since they may be used in 
irregular cavities, and in those opening downward; they may 
also be rammed after loading so as to increase the value of A . 

The advantages in this respect of the liquid state of nitro- 
glycerine made it very popular at first; but its tendency to 
leak in transportation and to filter through crevices in the 
rock is very objectionable, since in a thin film it is easily 
exploded by impact and especially so by friction. Cans 
containing it have been exploded by twisting the cork. The 
granular form is advantageous on account of the ease with 
which it may be loaded into bottle shaped cavities, as in 
hollow projectiles and torpedoes. Rigid prisms form con- 
venient packages for transportation, but require cavities 
of a special form to develop the best results. 
Cold. 

When in a liquid or plastic form, the high explosives have 
their sensitiveness much impaired by freezing. This occurs 
at a little above 0°. 

The force and sensitiveness of loose dynamite are not im- 
paired by its freezing. 

Heat. 

In such cases thawing is dangerous unless very gradually 
performed, as by the heat of the body, of manure, or of luke- 
warm water. 

The nitro-glycerine in frozen dynamite of the solid form 
tends to exude on thawing. 

The sensitiveness of an explosive increases with its 
temperature. 
Water. 

Nitro-glycerine and gun-cotton are insoluble. Water tends 
to displace the nitro-glycerine from dynamite' which has been 



XTV. — HIGH EXPLOSIVES. 



compressed; but, strangely, has no such effect upon that 
which is loosely granular. For this reason sub-aqueous 
torpedoes are charged with loose dynamite. 

Owing to its greater density the displaced nitro-glycerine 
settles to the bottom of the vessel containing the dynamite, 
whence it may exude and lead to the consequences noted 
above. 

When dynamite or gun-cotton is wet, it ignites with great 
difficulty but may be detonated by a powerful primer. Any 
soluble addition is of course removed by water. 
TTse. 

Except gun-cotton and the picrates, all the high explosives 
have so far been employed only for mining and demolition, 
and to a limited extent in pyrotechny. 

Efforts are constantly making to adapt them to the burst- 
ing charges of hollow projectiles, by affecting either their 
condition, the construction of the projectile, or the source 
of energy by which it is thrown. 

Such attempts have not yet (1888) wholly passed beyond 
the stage of experiment and, though occasionally successful, 
have yet to endure the test of long continued firing. In 
many cases it appears that failure comes less from explosion 
under the initial shock than from the friction due to the 
rotation of the projectile. If the initial shock or acceleration 
be diminished, flatness of trajectory is sacrificed or the gun 
is made inconveniently long; if the rotation of the projectile 
is abandoned, inaccuracy results. 

The sensitiveness of the explosive tends to cause a prema- 
ture explosion on impact against armor and its force tends 
to pulverize the envelope into ineffective fragments. 

The sphere of such explosives appears to be confined to 
the ordinary sub-aqueous mines or to their employment in 
aerial torpedoes, exploding under water in the vicinity of a 
vessel, as in the Zalinski system; or against earth works as 



XIV. — HIGH EXPLOSIVES. 



in the new gun-cotton shell now employed in Germany. 
This projectile has been fired with charges as great as 
110 lbs. Captain Zalinski has fired a mixed charge of high 
explosives weighing 500 pounds to a distance of one mile. 

Some of the high explosives, notably the gun-cotton class, 
have been used for fire arms, principally in fowling pieces, 
for which the reasons assigned, Chap. XI, page 18, particu- 
larly adapt them. The absence of smoke is a considerable 
advantage. They have even been employed by the Austrians 
for field pieces. 

The uncertainty as to the order of the explosion resulting 
from accidental variations in the value of A , has caused their 
use in cannon to be abandoned. For the former purpose it 
is still unfortunately common. 

GUN COTTON. 
Forms. 

This occurs in three forms; viz.: 

1. In the flocculent or pulverulent form, made from cotton 
wool as indicated in the chemistry. 

2. Prepared from the first form by pulping and com- 
pression to a density a little greater than that of water. 

3. In grains, made by disintegrating the second form 
above. 

Condition. 

The first form is always used dry and is employed only in 
pyrotechny. The other two are used either wet or dry, and 
when wet, are sometimes protected by a water-proof coating 
to retard evaporation. 
Firing. 

Dry gun-cotton ignites at a lower temperature than any 
other of the common explosives. Its combustion may be 
retarded by compression and the addition of a gum. 

When it contains from 20 to 30 per cent of water, it can- 



XIV.— HIGH EXPLOSIVES. 



not be ignited until the water has been evaporated by the 
flame. One ton of loose wet gun-cotton has been burned 
with safety in a bon-fire 
Detonation. 

When wet and compressed, it may be detonated by using 
a sufficiently large primer of dry gun-cotton. Its incorpo- 
ration in a dry state with paraffine is said to yield the same 
results as to safety as when it is wet, without diminishing 
its sensitiveness to detonation. This avoids the difficulty 
of preventing evaporation. 
Reaction. 

This varies with the value of A and with other conditions, 
but may be represented by the following formula, 
2QH7(N02)3 05=70H2H-3C02 + 9CO + 6N. 

To increase its potential a nitrate or chlorate is often 
added, the latter being the more energetic. 

Gun-cotton mixed with one third its weight of a nitrate 
forms Tonite, an explosive much used in the Californian 
mines. 
Advantages. 

Compared with gunpowder, its manufacture is less danger- 
ous and the apparatus can easily be improvised from the 
paper-mills. 

Since it forms no dust and can be kept wet, it is safe in 
transportation and in store. 

In mining, as in fire arms, it yields no solid products, and 
in sub-marine mining it can be used under water; having 
even been detonated in a net. 
Disadvantages. 

Besides those which relate to its sensitiveness and vio- 
lence, the principal objection to its employment in artillery 
applies to the absence of smoke which serves to mark the 
bursting point of a distant shell. 



10 XIV. — HIGH EXPLOSIVES. 



MANUFACTURE OF GUN-COTTON, 

rormer Method. 

Gun-cotton, like nitro-glycerine, was discovered about 
1846. It was first made by dipping cotton wool into mixed 
sulphuric and nitric acid and washing thoroughly the gun- 
cotton wool so formed. But it was found to be impossible 
to remove the free acids from the tortuous capillary tubes 
of which cotton wool is composed, and the resulting product 
was dangerous in store. 
Abel's Method. 

The tim? of manufacture has been much reduced and the 
quality of the product improved by the following method. 

Instead of using raw cotton, often containing impurities 
which are liable to cause spontaneous decomposition, cotton 
waste is employed. This has been previously spun mto 
yarn for cloth and is therefore mechanically clean. 
Preliminary Operations. 

Its conversion into gun-cotton follows the method previ- 
ously taught, the essential points being: — 

1. To prevent the continued action of dilute acids and 
the consequent formation of di-nitro-cellulose (Collodion 
cotton), by removing the cotton after its first immersion 
to a fresh mixture of acids in which it is soaked for several 
hours. After each immersion the excess of acid is removed 
by wringing. 

3. To prevent an undue rise in temperature, by making 
the first immersion in small quantities at a time, and sur- 
rounding the vessels containing the cotton with running 
water. 

3. To prevent the access of water to these contents. A 
drop of sweat may cause the acid cotton to ignite. 
Final Operations. 

After the final wringing, it is washed by plunging small 
quantities of the cotton into large quantities of water. 



XIV. -HIGH EXPLOSIVES. 11 

The cotton is then reduced to a pulp by the rotary knives 
of the rag engine used in paper making. These operate 
under water. 

Being now in short tubes, the washing can be thoroughly 
performed by means of the paper maker's poacher. This is 
a vertical water wheel working on one side of an oblong 
trough through which a longitudinal partition extends 
nearly from end to end. 

After a protracted washing in the poacher, the free acids 
still remaining are neutralized by some alkali; this having 
been washed out, the pulp is, after draining, ready for the 
hydraulic press. 

After pressing the cylinders they are carefully and slowly 
dried; or, they may be kept wet as previously stated. 

A similar product has been made from bran or straw, and 
is known djs, fulmi-bran^ etc. 

NITRO-GLYCERINE. 

Manufacture. 

The preparation of this explosive has been sufficiently 
described in the course of chemistry The principal points 
to be observed are: — m 

1. To prevent a rise in temperature by pouring the 
glycerine slowly into the mixed acids, and to preserve a low 
temperature by a jacket of running water and by agitating 
the mixture by a current of air. 

2. To wash the product thoroughly with cold water and 
finally with an alkaline solution. The addition of cold water 
precipitates that portion of the nitro-glycerine which remains 
suspended in the heavy acid liquid. 

Too much importance cannot be attached to the entire removal 
of free acid. The detection of free acid constitutes one of 
the most important tests of this product. 



12 XIV. — HIGH EXPLOSIVES. 

When first made, it is white and opaque; \t soon assumes 
an oily appearance which, if well made, it retains. Its density 
is about 1.6. 

Reaction. 

The explosion of nitro-glycerine gives the following 
reaction, 

2C3H5(NO,)3 03=6CO,+ 6N4-0 + 5 0H«. 

Following a general law, since its composition furnishes 
an excess of oxygen, the reaction is sensibly constant and is 
found to agree with that deduced on theoretical grounds. 
In this respect it differs from most of the explosives. 

Special Properties. 

As ordinarily used, this is the most powerful of the ex- 
plosives, excelling both in potential and force. 

It was originally thought to be perfectly safe when frozen; 
but it has since been found that, when in this condition, it 
can be exploded by a powerful shock if concentrated upon 
a mass sufficiently small. 

DERIVATIVES OF NITRO-GLYCERINE. 

Owing to the dangerous properties of liquid nitro- 
glycerine, it is no longer employed except with an absorbent 
dase or dope which will prevent its exudation. 

The absorbents are of two kinds: — 

I. Those which are chemically inactive, such as kiesel- 
guhr (also known as " tripoli " and " electro-silicon "), mica- 
ceous scales, and, for its alkaline properties, magnesium 
carbonate. 

II. Those which are chemically active. 

These derivatives have a density of about 1.6. They are 
usually plastic, which gives them great practical utility. 



XIV. — HIGH EXPLOSIVES. 13 



I. MECHANICAL ABSORBENTS. 

Dynamites. Giant Powder. 

Of these absorbents the best is kieselgiihr. This consists 
of microscopic shells, the cavities in which retain the liquid 
and protect it from ordinary shock. Kieselgiihr has remark- 
able properties as an absorbent; it can take up three times 
its weight of nitro-glycerine without exudation, even when 
under considerable pressure. 

Different grades of dynamite are made depending upon 
the proportion of nitro-glycerine which they contain. The 
highest is called No. 1. 

Owing to the knowledge of the properties of this explosive, 
gained by the torpedo service and by private industry, it 
may be called the standard high explosive of the United 
States. For torpedoes its merits consist in: — 

1. Its force. 

2. Its permanency under the varied conditions and 
accidents of service. 

3. Its safety and convenience in loading. 

4. The readiness with which it may be procured in the 
market. 

This was true in 1881. Since then several explosives have 
been invented which threaten its supremacy, 
Preservation. 

Although used for special purposes in the granular form, 
in which it resembles brown sugar, it is generally put up 
compressed in cylinders wrapped tightly with paraffined 
paper. These are packed in sawdust in wooden boxes, 
preferably made light, without metallic parts and coated in- 
side with a water-proof varnish. 

When received, the boxes should be partly opened to 
facilitate the discovery of the nitrous fumes that accompany 
the process of spontaneous decomposition. Their contents 



14 XIV. — HIGH EXPLOSIVES. 

should be tested for exudation and acidity, and should be 
carefully kept from water, 

• II. CHEMICAL ABSORBENTS. 

Properties. 

Absorbents of this class reduce the quantity of nitro- 
glycerine required to produce a given effect and so cheapen 
the product. 

Their judicious selection adds greatly to the energy 
developed by the nitro-glycerine alone, so that the economic 
value of the explosive may increase more rapidly than does 
'its percentage of nitro-glycerine. 

For sub-aqueous explosions it appears that with any par- 
ticular base there is an economic gain in increasing the per- 
centage of nitro-glycerine up to a certain point, but that 
beyond that point the advantage ceases. There appears to 
be a decided advantage in gelatinizing the nitro-glycerine 
before its absorption. 

See Forcite and Explosive Gelatine, /<?j/. 

Classification. 

The chemical absorbents may be conveniently divided 
into two general groups, according as they are simply com- 
bustible, or in themselves high explosives. 

Class I. A combustible dope. 

When finely ground cellulose is treated with super-heated 
steam, it is converted into a jelly capable of absorbing 19 
times its weight of nitro-glycerine. With or without the 
addition of nitre, it forms Foi^cite^ a most powerful explosive. 

Gunpowder, preferably made after Col. Wiener's method, 
Chap. IV, may be coated with nitro-glycerine, the detonation 
of which detonates powder, Chap. XI, This foruas the 
Jtidson powder. 



Class II, A high explosive as a dope. 

The most famous is known as Explosive Gelatine. This 
consists of about 93 per cent of nitro-glycerine with 7 per 
cent of collodion gun-cotton (di-nitro-cellulose). The 
addition of 3 or 4 per cent of camphor greatly diminishes 
its sensitiveness and adapts it particularly for warfare. 

It is generally a transparent jelly, but often becomes hard 
and opaque. The fulmi-bran, page 11, may replace the 
collodion cotton. 

Although found by General Abbott to be stronger than 
nitro-glycerine, it is much safer, particularly against shock. 
It has been found to burn freely without explosion, even 
when confined, and to resist perfectly the action of water. 

It requires an initial primer for its detonation and the 
weight of the primer required increases as its sensitiveness 
diminishes. 

When the collodion cotton is not thoroughly purified, this 
explosive tends to decompose spontaneously. Otherwise it 
is quite stable. 

New smokeless powder. 

By reversing the proportions of nitro-glycerine, and col- 
lodion used in explosive gelatine, and retaining the camphor, 
the compound becomes plastic when heated. It may then 
be pressed into sheets or drawn into wires or rods which, on 
cooling, become horn-like, like the celluloid of commerce. 

The reduction of w and the increase of \i are reported to 
give in the 6 in. Rifle a value oi %•=. 100 -f-. Its tactical 
advantages adapt it particularly to rapid firing arms of small 
caliber. The special difficulties to be overcome refer to the 
volatiUty of the camphor and to the erosion of the bore re- 
sulting from the heat of the explosion. See Chap. IX, Notes. 

NITRO-BENZINE OR -BENZOLE. 

The preparation of this resembles that of nitro-glycerine, 



16 XIV. HIGH EXPLOSIVES. 



the mono- (liquid), and di-, and tri-nitro benzines, (crystal- 
line) being formed. (Bloxam, Art. 325.) 

These substitution products are in themselves inexplosive, 
and show by their composition, C^ H^(N02)g_j, ^^^ necessity 
for the addition of an oxydizing agent. 

Rack-a-Rock is made at the time of its employment by 
saturating K CIO3 with crude mono-nitro-benzine, or even 
with the "dead oil" from the gas works which has been 
diluted with CSg containing a small proportion of sulphur. 
By exposure to the air the CSg evaporates, leaving the finely 
divided sulphur on the salt but protected by the lubricating 
property of the oil or nitro-benzine against explosion by 
friction. 

When the dope is finely ground and the charge exploded 
by a powerful primer it is found to be nearly as powerful 
as dynamite No. 1. 

This is the only chlorate mixture which has been found 
safe in practice. 

Helhofite^ as used in Germany for armor piercing pro- 
jectiles, is another of the Sprengel Safety Mixtures pre- 
pared as wanted by dissolving di-nitro-benzine in nitric acid. 

Bellite (La.tin: Bel/um — War), is a recent Swedish explosive 
made of about -J tri-nitro-benzine and | ammpnium nitrate, 
incorporated together. 

This is distinguished by its great safety under all con- 
ditions and by its greater potential as compared with 
dynamite, 

Only dampness affects it. It is almost incombustible, 
smouldering only by the continued application of flame. 
It is so insensitive to shock that the detonation of itself upon 
a box filled with the explosive, or the explosion of gunpowder 
in its midst fails to explode it. A wad of it has been fired 
from a fowling piece against a target without injury to either. 
It gives no injurious gases, nor flame, which properties. 



XIV. — HIGH EXPLOSIVES. . 17 

together with its high potential, particularly adapt it for the 
coal miner. It is also cheap and indifferent to variations in 
temperature. 

Tamping is necessary to develop its full effect, even when 
detonated ; but when tamped and detonated, it is about 33 
per cent stronger than dynamite. 

The crystaline form of the two ingredients of Bellite 
would appear to insure its stability in store and to make of 
it one of the best high explosives where potential is required, 
as in torpedo shells. For sub-aqueous mining, dynamite is 
probably better suited. 

PICRIC ACID (TRI-NITRO-PHENOL). 

This is made by the action of nitric acid on carbolic acid 
(phenol). It occurs in slightly soluble plates of a bright 
yellow and is much used in dyeing. Unconfined, it will not 
explode by heat, but may be detonated. 

When mixed with gun cotton dissolved in ether, it is said 
to form the new French explosive, Melinite. 

Emmensite is a recent American explosive, prepared from 
crystallized Emmens acid and a nitrate. The acid results 
from the solution of picric in nitric acid. 

The claims made for this explosive resemble those noted 
under the description of Bellite. It is (1891) under trial in 
the United States. 

THE PICRATES. 

The potassium and ammonium salts are the only ones 
employed. 

The former with the addition of nitre and charcoal forms 
Designolle's powder. This was found too dangerous for 
use, as it tends to detonate on ignition. 

The ammonium salt is less sensitive to shock and burns 
in the air like resin. With the addition of a nearly equal 



18 XIV. HIGH EXPLOSIVES. 

part of nitre and prepared like ordinary gunpowder, it forms 
the powder of Briigere. In small arms, a charge less than 
one half the charge of ordinary gunpowder suffices to pro- 
duce the same effects. This is of importance since it enables 
the size and weight of the cartridge used in magazine rifles 
to be greatly reduced. 

The powder yields no smoke or fouhng but is hygroscopic. 

It is believed that the new powder used in the French 
Lebel rifle is a variety of Brugere powder. 

THE FULMINATES. 

The mercuric salt is the only one of practical value. Its 
efficiency depends rather upon its force and the nature of 
its product than upon the heat evolved by its decomposition. 

This follows from the reaction, 

C2HgN2 0a=:2CO + Hg + 2N. 

Its force is said to be nearly 10 times that of gunpowder. 

When dry it is easily detonated by shock, friction, a tem- 
perature of about 200°, or by the strong acids. 

Certhelot finds that even so stable a gas as nitric oxide 
is dissociated by the detonation of mercuric fulminate. 
While for detonation it is preferably used pure, for igniting 
the charges of fire arms it is mixed with an oxydizing agent 
and often a combustible, in order to increase the length of 
the flame. Powdered glass 's also added v/hen the salt is 
expiod'^d by percussion. 

Its safety in manufacture depends upon its absolute in- 
explosiveness when wet. If placed upon a metallic surface, 
it tends to decompose; hence, percussion caps are varnished 
before they are primed. 

Under no circumstances should the fulminate be carried or 
stored near any of the high explosives. 



XIV. HIGH EXPLOSIVES. 19 



CHLORATE MIXTURES. 

Since their discovery, a century ago, frequent efforts have 
been made to utilize the chlorate mixtures in mining and as 
a substitute for gunpowder. Their extreme sensitiveness 
to friction has almost uniformly caused their employment 
for such purposes to result in disaster. 

Mixed with Sbg S3, the potassium chlorate forms the friction 
composition used in cannon primers. It is also employed in 
pyrotechny to compensate for the cooling effect of sub- 
stances employed to give color and brilliancy to the flame. 

GENERAL REMARKS ON THE EMPLOYMENT OF 
THE HIGH EXPLOSIVES. 

In Guns. 

Their employment has always failed, except for small arms 
and as noted page 8. 

For Bursting Charges of Hollow Projectiles.* 

Explosive gelatine has been occasionally fired without 
premature explosion, by the use of diaphragms within the 
shell. See also gun-cotton, and the experiments with the 
Zalinslii gun before noted. 

For Demolition of "Walls, etc. 

Unless the wall is very strong, the best results in breach- 
ing appear to follow the detonation of the explosive at the 
base of the wall and at a few inches distant. This distrib- 
utes the effect, and racks and fissures the wall so as to facili- 
tate its destruction by hand. 

Exploded in immediate contact, a smaller hole is said to 
be made and the energy to be expended in giving motion 

* The premature explosion of such bursting charges by the shock of 
discharge is often attributed to the sensitiveness of the fulminate neces- 
sarily used in the detonating fuze. 



20 XIV. — HIGH EXPLOSIVES. 

to but few fragments. About 10 lbs. of dynamite will open 
a practicable breach in a two foot stone wall. Tamping 
would reduce the size of the charge required. 
Houses, Palisades, etc. 

About 5 lbs. of dynamite will wreck a small stone dwelling 
if exploded near its center, since it tends to overthrow all 
the walls instead of blowing out through the nearest one. 
The same quantity suffices for a linear yard of ordinary 
palisading. A pound of dynamite will shatter a 12 inch 
bridge timber.* 
Disabling Cannon. 

When time permits, bring the gun as nearly vertical as 
possible; fill it with water, plug it, and explode simultane- 
ously two one pound charges of gun-cotton, one at the 
bottom of the bore and one in the chase. When time is 
scant, insert a shot within the bore, and place on top of the 
chase, between the shot and the muzzle, two pounds of gun- 
cotton, laying over it a filled sand bag or a sod. Such charges 
are said in the English Manual to suffice for the lighter 
natures of sea coast guns. 

It is found to be more advantageous to attack the cannon 
themselves, than to waste time and explosive material on 
their carriao:es. 



♦These directions are intended to apply only to hasty operations. 
When time permits, the best results will follow from placing the charge 
under or within the structure to be demolishedo The quantities are 
approximate. 



XV. — M£T ALLURG Y. 



CHAPTER XV. 
METALLURGY. 

I. TESTING MACHINES. 

Necessity. 

The physical properties of a metal may sometimes be in- 
ferred from a knowledge of its chemical composition, but so 
many other causes may contribute to modify these properties 
that chemical analysis should be depended on, rather to indi- 
cate the existence of certain limiting or possible conditions 
than to declare the extent to which these conditions have 
been approached. Thus, what a metal is becomes subordi- 
nate to what it can do ; and its proof is more conclusive than 
even its chemical inspection. 

Requisites. 

A complete testing machine should include means for de- 
termining the varying strains under tensile, crushing, trans- 
verse, torsional, and shearing stresses. But for simplicity, 
and on account of the comparative ease with which all stresses 
can be referred to that first named, such machines are gen- 
erally of the tensile type. 

Comparisons. 

For establishing comparisons the stresses are usually meas- 
ured per unit of minimum area of cross section, and the 
strains per unit of length between established points on the 
specimen. But if the form and dimensions of the specimens 
are constant, absolute measures may be compared. In the 
following discussion stresses and strains will, unless otherwise 
stated, be taken per unit of section and of length. 



XV. — metallurCV. 



In the United States stresses are given in pounds per square 
inch; in England in tons of 2240 lbs. per square inch; in 
France in kilogrammes per square centimetre; in Russia and 
Germany in atmospheres. 

Form of Specimen. 

Since the deductions from proof are conclusive only as to 
the actual piece tested and are inferential as to all others, 
the above precautions for the comparison of properties are 
not wholly sufficient. The general • rule in experimental 
comparisons, of dealing with but one variable at a time, 
should be followed by subjecting specimens as nearly as 
possible in size and shape lik>e those to be actually employed 
to the same kind of stress that they will be called on to sustain. 

But the capacity of the machine rarely permits this, and, 
as its strength limits the maximum cross section, the length 
of the specimen in units of the corresponding diameter should 
be approximately proportional to that of the finished piece. 
The size of the machine and the cost of preparing specimens 
limit this; so that the length of the specimen is generally 
about 4, 6, or 8 diameters, with a tendency to increase. 

The specimen is held so that its axis coincides with the 
action line of the force; otherwise, it will rupture in detail, 
or tear across. This condition is fulfilled by making the 
specimens truly cylindrical with enlarged concentric heads, 
figure 3, by which they may be held in the machine. 

Form of Record. 

This states the strains due to certain stresses. They are 
functions of each other, and the relation may be expressed 

e —f{w), 

in which e represents the strain, or the change of form pro- 
duced by applying the stress w. The stress is taken as the 
independent variable since it can be more readily controlled 



XV. — METALLURGY. 



than the strain. Inasmuch as conditions vary too much, and 
are not yet sufficiently understood to enable the law of this 
function to be analytically expressed, that which governs any 
particular case may be best determined empirically: 

1st. By forming successive orders of difference in the 
observed value of the function for equal increments of the 
variable w. 

2d. By plotting a line constructed from these co-ordinate 
values. Such a line is called a strain diagram. 

3d. By constructing a strain diagram automatically during 
the progress of the test. 

The order of preference is as follows: 

The first method when great accuracy is required and 
when a micrometer can be used. 

The second and third when general comparisons are to be 
made. 

The second to the third when the expense of the registering 
apparatus is objectionable. 

In general, rectilinear strains can be measured more accu- 
rately than they can be registered by any mechanical apparatus. 

ELASTICITY. 

Elastic Limits 

In operating the machine the stress is very slowly and stead- 
ily applied, either directly by hydraulic pressure, or indirectly 
by a screw acting in combination with levers. The stress is 
relieved at intervals and the specimen permitted to recoil. 

The difference between the strain e and the recoil r is the 
set s, ov e = r -\- s. The set may diminish in time and be- 
come the permanent set, but the first temporary set is that 
generally recorded. Sets probably occur under all stresses, 
but may be too small for measu^-ement. This may be illus- 
trated by the curves, figure 1, which are very much exagger- 
ated. 

Let 00\ 00" represent certain stresses resulting in strains 
O'p' , 0"p'\ etc. Each of these strains is by definition com- 



XV. — METALLURGY. 



posed of the recoil r — r'p' and the set s = O'r' , etc. 
Starting from 0, as the stresses increase the recoils and sets 
both increase, but the sets less rapidly than the recoils. 

After a certain stress, Z, the line of sets becomes nearly 
parallel* to that of strains, so that for a given increment of 
stress the increments of strain and set are nearly equal. The 
stress corresponding to L is the superior limit of the stresses 
for which the sets increase less rapidly than the recoils, and 
the inferior limit of those for which the sets increase more 
rapidly than the recoils. This stress is called the Elastic 
Limit. 

Since below the elastic limit the sets are relatively small, 
and above it the sets are relatively large, when compared 
with the recoils, it may be defined as the limit of the stresses 
within which sets may be neglected and beyond which recoils may 
he neglected ; or the limit separating the consideration of the 
elasticity of the metal from that of its ductility. 

It may be determined — 

I. By finding the stress corresponding to the first significant 
term of the second order of difi"erences of strains or sets. 

II. By inspection of a diagram such as represented in fig- 
ure 13. 

Coefficient of Elasticity. 

If the strains below the elastic limit be considered directly 
proportional to the stresses, this portion of the line will be 
straight, and the tangent of the angle included between it and 
the axis of E will be proportional to the reciprocal of the 
rate at which the specimen submits to (i.e., directly to the 
rate at which it resists) the stress. This is called the coeffi- 
cient of elasticity, or 

^ _ r^ _ ^ ^ /Wheeler, \ 
^ ~ Z ^ 7 ' V Eq. 1. y 

* As a rule, the recoils increase gradually throughout. 



XV.— -METALLURGY. 



Elastic Work, etc. 

The area bounded by the diagram, the axis of E, and a 
line drawn through any point of this axis parallel to the axis 
of PFis evidently proportional to the work done by the corre- 
sponding stress. 

For a given stress O O'", the area, O e r"', is proportional 
to the work of permanent deformation corresponding to the 
stress O O'". Similarly the difference between the areas 
0^'/'"and O^r'" is proportional to the work of restitution, 
or the elastic work, following the same stress. The term 
Elastic Work, as a measure of this elastic property, also 
known as toughness, is properly applied only to the area 
under the diagram at the elastic limit. 

The total area under the diagram up to the point of rup- 
ture is proportional to the potential work of deformation. While 
for mechanical units, such as posts, beams, levers, chains, this 
property is valuable; in the more complex structures required 
by the principle of the independence of function, such as 
wheels, trusses, and built-up guns, the elastic work, which 
comprises in its measure both the elastic limit and the coeffi- 
cient of elasticity, is much more important. 

In such structures the permanent change of form of one of 
the units may derange the rest; and generally the elastic 
work may be counted on repeatedly, while the work of per- 
manent deformation can be utilized but once. 



FORMS OF TESTING MACHINES. 

Tensile. 

This is the form most generally used and upon the indica- 
tions of which modern gun construction is based. 

The sketch, figure 2, shows a simple apparatus extempo- 
rized for testing the sheet metal from which small-arm car- 
tridges are made. The strains were taken from the punch- 
maVks a,b, and plotted. 

For testing the metal of which cannon are made, a form of 



XV — METALLURGY. 



tensile machine recently devised in England consists of a 
hard steel cone, which by a blow from a falling weight is 
driven through a ring cut concentrically from one of the 
short cylinders composing the gun. 

Transverse. 

The simplest of all is for transverse stress. The specimen 
is placed on rollers kept at a constant distance apart. One 
objection to transverse machines is the difficulty of separating 
the tensile from compressive strain. 

A valuable modification of this form of machine is that 
which tests the capacity of the metal to endure extreme bend- 
ing, even to the extent of working its ends back and forth as 
long as the tenacity of the specimen permits. The bending 
angle thus determined is one of the readiest and best tests for 
ductile material. 

Torsional. 

Although a torsional strain is even more complex than the 
transverse, yet, owing to the ease with which the power 
of the lever may be increased; to the simplicity, compact- 
ness, cheapness and rapidity of operation of machines of this 
class; and to the ease with which the relative rotary motion of 
the parts may be made to record the circumstances of the 
test, this method is very valuable where great accuracy is not 
required, nor variation in the form of the specimens expected. 

For the machine used in this department of instruction, the 
specimens are of the standard size shown in figure 3. This 
requires direct comparison of results. 

Thurston's autographic torsional testing machine, fig- 
ures 4, 5^ G, 1, 8. 

Description. 

Two similar wrenches with rectangular jaws, facing each 
other, are carried by the A shaped frames shown in figure 4, 
and revolve independently about axes which are in the same 



XV. — METALLURGY. 



Straight line. The wrenches are not connected except by the 
interposition of the specimen, which is supported axially by 
the conical points shown, and kept by folding wedges from 
revolving in the jaws. The' arm B of one wrench carries a 
weight W at its lower end. The other wrench is revolved by 
a worm gear, P. 

To the frame A is secured a guide curve G, of such form 
that its ordinates are proportional to the successive torsional 
moments exerted by B during its revolution. 

The pencil-holder/^ is carried on the arm B, to which it 
is pivoted at a and b so as to oscillate in a plane perpendicu- 
lar to that in which B rotates. A spring, sp^ keeps the pen- 
cil-holder in contact with the guide curve. 

Operation. 

As the worm gear revolves it tends to revolved and to raise 
PTby means of the specimen -S". 

As B revolves, the roller r rides on the edge of G so that 
the pencil is displaced laterally in a plane perpendicular to 
that of its rotation; the object being to establish as follows a 
system of rectangular co-ordinate axes of stresses and strains, 
to which the position of the pencil may be referred: 

I. To make the lateral displacement of the pencil propor- 
tional to the stress, W. Since PTis proportional to the mo- 
ment of ^, which, since the weight of B is constant, is pro- 
portional to the sine of the vertical angle 0, figure 7, the 
edge of G is so formed that when B is rotated, the pencil 
will trace upon the cylinder D a curve the equation of which 
when developed on a plane surface is _y = ^ sin 0. In 
this equation J/ is the variable ordinate of the curve measured 
along that rectilinear element of D upon which the pencil 
rests when the inclination of ^ = 0, and <2 is a coefficient 
depending upon the maximum value of _y permitted by the 
construction of the machine. 

II. To make the peripheral displacement of the pencil 



XV. — METALLURGY. 



proportional to the strain, E. Calling ;t: the developed path of 
the pencil along a circular element of the cylinder, we have 

X '. (p>^ \\%TCr \ 360°, or0 =-— jvand .'.y=^ as'ml- .x\ 

^ ^ %7tr -^ \Z7tr j 

The circumference of the drum is 36 inches and its length 
is 5 inches; therefore, taking x in inches. 

jj^ = 5 sin (10 . x). 

Such a curve having been constructed upon paper may be 
wrapped around D, and the edge of G be adjusted so as to 
make the point of the pencil follow the curve as B is revolved, 
D being at rest. 

The strain is evidently proportional to the rotation of D 
relatively to that of the pencil ; while the stress is proportional 
to the angular displacement of the pencil. This will be un- 
derstood by imagining lines traced by specimens which are 
either perfectly extensible or perfectly inextensible. Such 
lines are limits for all natural specimens which will cause in- 
termediate lines to be traced that will express the relation 
e ^/{w). 

Form of Record. 

The record is made on a piece of cross-section paper ruled 
in inches and tenths w^rapped tightly around the cylindrical 
drum D. 

The weight W is so taken that the maximum moment 
= 500 lbs. ; therefore, since the ruling is 5 inches wide, one 
division of the paper measured across its width represents a 
moment of 10 lbs., and, since 2 tt r = 36 inches, one division 
along the length of the paper = 1° of strain. 

In raising the arm by the specimen, the moment of W is 
in equilibrio with the torsional stress plus the frictional mo- 
ment of the journal /; this last is constant and is allowed 
for in standardizing the machine. 



XV. — M£tALLURGY. 



INTERPRETATION- OF THE RECORD. 

For torsional test this is facilitated by considerinij the spe- 
cimen as consisting of parallel fibres, at first rectilinear, and 
elongating under stress in a helical form. The general form 
of strain diagrams, whether made by torsional or tensile test, 
is so similar, that although the following discussion partic- 
ularly refers to the results of the torsional test, its application 
may be considered as general.* 

General Case. 

The combined effect of stress and strain is seen in the 
typical diagrams, figure 9. 

In curve / the elastic limit is plainly shown at a. The 
convexity of the first portion is probably due to the prelimi- 
nary strain of the exterior fibres occurring in soft materials. 

The line then becomes sensibly straight, its inclination 

determining the coefficient of elasticity, -— , or the rigidity 

of the specimen. Beyond the elastic limit it becomes wavy, 
indicating deficient homogeneity as to structure ; the fibres 
are then supposed to slip. Having adjusted themselves they 

* The following relation between torsional and tensile stress has been 
approximately determined by experiment. Let T = tensile stress in 
lbs. per square inch; Ti = torsional stress in lbs. ; 9 = angle of torsion 
in degrees. Then, for steel and probably for other ductile metals, 

T= 7\ (300 -^\. 
For cast iron, 

r=n(soo-^)^|. 

The extension of an external fibre and the reduction in area of cross 
section corresponding to torsional strain are given in tables furnished 
with the machine. For ultimate extensions the value of correspond- 
ing to the maximum and not to the ultimate ordinate is taken. 



10 5tV. — METALLURGY. 



work together, as shown by the subsequent regularity of the 
Hne. 

At some point b the stress is relaxed, and the pencil falls to 
some point c ; when the stress is re-applied, the pencil rises in 
the line cb and continues nearly parallel to the straight por- 
tion of the line Oa until it reaches its former height db. 
The ordinates then slowly increase until, by the successive 
rupture of the concentric fibrous layers, the curve terminates 
at/ 

Note the total work Oabefg 0\ the elastic work OaL; 
and the recoil dc and set Oc for the stress db. The parallel- 
ism oi be to O'a shows the practical constancy of the co-- 
efficient of elasticity under varying stresses provided the total 
elongation be diminished by the set. By some, this coefficient 
is considered the most permanent physical characteristic of 
steel, in various forms of which it has been found to vary less 
than 8 per cent, in specimens whose elastic limits varied 200 
per cent. 

The point ^ is a new elastic limit, and the entire line may 
be termed a locus of elastic limits. Of these the point a is 
called the primitive elastic limit, and the other points various 
special elastic limits. Notice that as these successively rise, 
the potential work diminishes. The special elasticity thus 
produced by stress, as distinguished from the primitive elas- 
ticity of the specimen, is treated of in gun construction. 

Some metals give a curve like //, in which it is difficult by 
either of the methods given, page 3, to determine the elastic 
limit. In such cases it is generally taken as the stress corre- 
sponding to the point of tangency of a line inclined at 45°. 

Graphical Representation of Special Physical Properties. 

Considering the diagram, figure 9, to represent that of a 
tensile instead of a torsional 'test, the principal properties of 
the specimen are graphically expressed as follows: 

The Tenacity, or the capacity to resist rupture by extension, 
is measured by the maximum ordinate at e. The correspond- 



XV. — METALLURGY. 11 

ing Stress may be greater than that at which fracture finally 
occurs. In such a case the form of the portion of the dia- 
gram, ef, indicates probably the progressive rupture of the 
final layers. 

The Elasticity, or the property of resisting permanent exten- 
sion or compression, as we have seen may be measured either 
by an absolute quantity, the elastic limit, or by a rate. When 
this rate is practically uniform, as in steel, page lo, the elas- 
tic limit alone may serve to measure the elasticity. 

The Ductility, or the property of submitting to permanent ex- 
tension, may also be measured by an absolute quantity, O g, 
or more exactly. Oh, figure 9; or by a rate. This rate- is 
measured by the cotangent of the angle made by the tangent 
to the diagram at any point beyond the elastic limit and the 
axis of strains. This measure, although not generally 
adopted, io important since it illustrates the phenomenon 
known as the flow of metals under stress. As seen in the 
following examples, this rate may vary not only in degree 
but also in its sign. 

Ductility, though useful in such arts as the drawing of 
wire and of metallic cups like cartridge cases, is now regarded 
only a secondary property of cannon metals. Cannon are so 
proportioned that the elastic limit is the superior limit of the 
applied forces, but the ductility of the metal is thought to 
give an additional safeguard against destructive explosion. 
But safety then depends rather upon the potential work of de- 
formation of which the metal is capable than upon either its 
tenacity or its ductility alone. 

Particular Cases. 1. Woods. 

To illustrate these remarks by reference to materials the 
physical properties of which are more generally known than 
those of the useful metals, the torsional diagrams of the prin- 
cipal woods used in ordnance construction are represented 
in figures 10, 11, 12. 

The woods are arranged from right to left in the order of 



12 XV.- METALLURGY. 



their coefficients of elasticity. This brings them approxi- 
mately in the order of hardness, or stiffness, black walnut 
leading. 

These qualities fit this wood to resist the abrasion to which 
gun-stocks are subject, and to give to the easily bent gun- 
barrel its necessary support. 

The elastic limits of cypress and black walnut are seen to 
be equal, but the cypress is much the tougher of the two. It 
appears to be about equal to a poor quality of oak, for which 
wood, in the construction of gun-carriages, it was formerly 
used in localities where oak could not be procured. 

The forms of the diagrams after passing the elastic limit 
•are very characteristic. In some cases, as in ash and white 
pine, the line continues for some distance parallel to the axis 
of strains. This would indicate the use of these woods for 
pieces which being long and slender are apt to be bent. 
When lightness is an object, as in the former case for wagon 
poles, sponge and rammer staves, agricultural-tool handles, 
and in the latter case for building purposes, particularly of 
railway carriages, the low density of these woods makes them 
highly esteemed. 

The sudden dip of dog-wood, oak, and hickory occurs in 
most hard woods. It is supposed to arise from the lateral 
slipping of the fibres, the cementing substance having given 
way. When this is brittle, as in the resinous yellow pine, a 
very sharp depression is sometimes seen. 

In some cases, as in dog-wood, hickory, and notably in 
elm, the line rises again, sometimes exceeding the elastic 
limit. The rise is supposed to be due to the retwisting of the 
fibres, separated at the elastic limit, into a consistent whole. 
On the other hand, the step-like decline of some of the dia- 
grams indicates the brittleness of the corresponding woods. 

The surprising qualities of dog-wood show that the small 
size of this tree is the principal bar to its utility. 

The importance of testing machines is very imperfectly ap- 
preciated among practical manufacturers. This appears from 



XV. — METALLURGY. 13 

one of the oak diagrams which was made by a piece taken 
from a new gun-carriage the stock of which was broken in 
two by firing. 

2. Metals. 

The diagrams in figure 13 will be referred to hereafter in 
discussing the metals represented upon them. To avoid 
confusion, curves of similar metals are arranged in groups, a 
new origin for each group being taken along the axis of 
strains. 



II. ORDNANCE METALS. 

The principal metals used in Ordnance manufactures are. 



Ferreous. - 



Steel I ^'^^' 

' ( low. Cupreous or 

Wrought Iron, Kalchoids. 

. Cast Iron. 



r Brasses, 
Bronzes 
and other alloys 
of Cu, Sn, Zii. 



Nomenclature. 

For clearness of definition by scientific men, the forgeable 
ferreous metals are proposed to be classified according to 
their mode of manufacture and according to their capacity to 
harden, and are designated as follows: 

1st. Those made from a pasty mass, by the prefix. Weld. 

2d. Those made by fusion, by the prefix, Ingot. 

3d. Those which will harden and temper by the usual 
treatment of steel, by the suffix, Steel. 

4th. Those which will not sensibly harden, by the suffix, 
Iron. 

5th. The only unforgeable ferreous cannon metal is cast 
iron, known in the crude state as pig-iron and after remelt- 
ing, as castings. 

This classification affords the following scheme; 



14 



XV.— METALLURGY. 











1 


cl 


-a 

OS 

O 










en 0) 

biDT3 


un-metal = 
•ass = 

•hosphor- or 
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.J 

< 
y 


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cu 


C 
o 
















!5 


1 


<D 
1/3 

Si 

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1 









XV. — METALLURGY. 15 



Relative Importance. 

Owing to their peculiar adaptability to the demands of 
construction, the ferreous ingot metals are gradually super- 
seding all others, and the time when they will be altogether 
employed except for subordinate purposes is delayed only by 
our imperfect knowledge of their properties. These metals, 
under the common name of steel, already cover in their 
application the wide range between castings for the frames of 
iron-clads, weighing many tons, figure 14, and horseshoe 
nails, the successful making of which was formerly considered 
the most severe test of the quality of wrought iron. The 
ages of stone, bronze, cast and wrought iron have been suc- 
ceeded by the age of steel. 

On this account the following discussion will relate princi- 
pally to steel. As a cannon metal it has only recently come 
into favor, having been considered brittle and untrustworthy. 
It is largely due to the patient genius of Krupp and Whit- 
worth that this prejudice has been overcome. 

As an example of the quality of modern gun steel may be 
mentioned the fact that it was found impossible to break a 
gun hoop under a drop giving a blow of nearly 100 ft.-tons, 
the arrangement being represented in figure 15. Sixty or 
seventy blows shortened the vertical diameter only half an 
inch. 



III. PROPERTIES. 

The useful properties of metals have regard to their 

1, Homogeneity, 



I. Constitution. 
{Jo be.) 



I. Chemical as to i o' n 

(2, Composition. 

( 1, Homogeneity, 

II. Physical as to -J 2, Structure, 

( 3, Strain. 



16 XV. — METALLURGY. 



II. Capacity for 
resisting. 
{To do.) 



I. Tensile j 1, Tenacity, 

Stress, or ( 2, Ductility. 

II. Compressive j 1, Incompressibility, 

Stress, I 2, Hardness. 

III. Either j 1, Elasticity, 

Stress, or ( 2, Homogeneity. 



III. Facility for being 
worked. 
{To suffer.) 



C 1, Fusibility, 

Hot, or \ 2, Weldability. 

( 3, Malleability (also cold). 

Cold, or 1, Annealability. 



/. CONSTITUTION OF STEEL. 
Metals should be homogeneous as to composition and struc- 
ture so as to be homogeneous as to strain. Those which 
have been fused are the most homogeneous ; but even they 
may be imperfect, both chemically and physically, as follows : 

I. CHEMICAL CONSTITUTION. 

1. Homogeneity. 

Pure iron can rarely be produced except by the methods 
of the laboratory, and therefore in exceedingly small quanti- 
ties. In practice it is combined with the most useful elements 
by heat, the fusibility of the alloy usually increasing with the 
number of elements contained. Fused metals in general are 
imperfect alloys, the constituents of which tend to arrange 
themselves according to their specific gravities. Due to the 
property of liquation, certain of the most fusible alloys of 
steel are found near the core of the ingot in greater propor- 
tion than elsewhere. Thus, in a steel ingot the parts first 
solidified represent most nearly its average composition, the 
centre of the bottom being the softest and that near the top 
the hardest, since the fusibility and the hardness of the alloy 
increase with the percentage of C* 

* Order of Oxidation. 

Reactions during fusion depend so much upon the order of oxidation 
of the constituents of pig-iron that the following approximate relation 
should be learned: 



XV. — METALLURGY. 17 



The segregation of the Kalchoids is very objectionable. 

2. Composition. 

The following elements occur in iron alloys : 
1. Carbon and iron as the principal constituents make the 
steel best suited for general purposes. It has often been tried 
to replace or supplement the action of carbon by other ele- 
ments such as silicon, tungsten, chromium, nickel, etc., but 
for general purposes carbon steel is far the most important. 

As a rule, the greater percentage of carbon up to about 
1.5 (and even 2 5 per cent.), or the higher the grade, 

The more — The less — 

1. hard and elastic ; 1. dense; 

2. tenacious ; 2. ductile ; 

3. brittle ; 3. weldable ; 

4. fusible; 4. forgeable, does steel be- 

5. expansible by heat, does come. 

steel become. 

The terms high and lotv referring to the grade of steel, or 
per cent, of C contained, are loosely applied, but the tendency 
is to draw the line at 0.35 per cent., where hardening by heat- 
ing followed by rapid cooling becomes perceptible. The 
following table exhibits the classification according to use. 
So much depends upon the percentage of hardening constitu- 
ents other than C, and upon the treatment of the steel in 
manufacture, that the relation expressed is only approximate. 



1. Silicon. 5. Iron. 

2. Manganese. 6. Phosphorus, in presence of an acid 

3. Phosphorus, in presence of slag; i. ^., one containing an 

an oxidizing basic slag. excess of S i O^. 

4. Carbon. 

These and other following relations depend so much upon existing tem- 
peratures and conditions that they are expressed in the most general terms. 



18 



XV. — METALLURGY. 



Grade. 



TABLE IL GRADES OF STEEL. 

Per Cent, of Carbon. Application. 



Low. 



High. 



Mild, 

Hard, 

Extra hard, 
Tool, 

Extra Tool, 
Die, 



Extra mild, 0.05 — 0.20 Boiler plates to be flanged, 

bridge material. 
0.20 — 0.35 Railroad axles, gun bar- 
rels, etc. 

0.35 — 0.50 Rails, cannon, etc. 
0.50 — 0.65 Springs, saws, etc. 
0.75 — 1.00 Chisels, cutters, etc. 
1.00 — 1.20 Files and very hard tools. 
2.50 Wire drawing, to resist 
abrasion. 

Carbon is generally supposed to exist in steel in two princi- 
pal forms: 1. Cement carbon^ characteristic of annealed or 
softened steel, and 2. Hardening carbo?i, characteristic of 
hardened steel. The former is insoluble and the latter is 
soluble in dilute H^ SO^. See page 48. 

The following elements are admitted, either of necessity or 
as Si physic ; i. e., replacing something more harmful or pro- 
ducing a beneficial effect. 

2. Silicon tends to displace C from combination, and to 
confer its properties, although in a less degree. 

It restores ''burned" or "rotten" steel by forming with 
the particles of iron oxide, to the dissemination of which 
this condition is often due, a fusible slag : 

{Fe^ O^ + Siz=zFe Si O^ + Fe), 

As Si increases the solvent power of steel for gases, and, 
by reducing the iron oxide present in the hquid steel, prevents 
the formation of CO it also prevents the honeycombing or 
vesiculation of the metal from the ebullition of the gases 
while the metal is becoming soUd. 

If uncombined, Si O^ may remain as grit, which is injuri- 
ous to the strength of the metal and destructive to cutting 
tools. 



XV. — MEtALLtJRGY. 19 



When in excess, Si makes steel brittle. This is generally- 
true of the non-ferreous ingredients of the alloy. 

3. Manganese, unlike Si, tends to make C combine with 
iron ; like Si, it tends to replace C functionally, but much less 
energetically. 

Afn resembles Si as a reducing agent, and forms with it and 
iron oxide a very fluid, cleansing, slag. 

The physical properties it confers vary with the proportion 
present. With from 3 to 6 per cent,, the steel becomes very- 
hard and brittle ; but with from 7 to 20 per cent, the steel 
becomes very tough and strong. 

Some Mn is necessary to prevent hoi-shortness, or the tend- 
ency to disintegrate when forged, even when no 6* is present. 
It also acts as an antidote to S, by forming Mn S, which is 
insoluble in melted steel. 

4. Phosphorus make steel cold short, or brittle at ordinary 
temperatures. It can be removed only by some basic process, 
as follows : Since the ordinary silicious, or acid, lining would 
prevent the oxidation of P, and, by wasting the iron, would 
increase the proportion in which P remained ; in the basic 
process the furnace is lined with dolomite brick. Iron ore 
and (for economy) limestone are added to the charge, so that 
the phosphoric slag that is formed may continue basic. 

The presence of Mn and Si in the pig iron from which 
washed pig is thus formed, protects from oxidation the C that 
it contains, and therefore maintains the fluidity of the charge, 
until the Mn and Si are consumed. When this happens and 
the bath boils with CO, the washed metal is cast into pigs 
containing only about 0.1 of the original P. 

So much C is retained that (after grading it by analysis) 
the washed pig is easily remelted in further processes relating 
to the manufacture of steel. 

These processes permit the use of pig iron, which was 
formerly too high in P. 



20 XV. METALLtfRGV. 



When added to the Kalchoids, P removes their greatest 
enemy, oxygen. 

5. Sulphur also is very difficult to remove, although the 
hot-shortness that it produces may be corrected with Mn or 
eliminated by Ca F^. 

6. Chromium increases the hardness of steel without im- 
pairing those qualities, such as ductility and malleability, 
which are incompatible with the hardness resulting from high 
carbon. 

7. Aluminium is said to increase the fluidity of low steel, 
and even of weld iron, in a remarkable degree, thus permit- 
ting the metal to be cast without danger from vesiculation. 
The fluidity of the metal in the mold permits the escape of 
the occluded gases. Its action on iron oxide resembles that 
of Si. 

A new alloy known as Mitis metal, which is thus formed, 
may be cast into the most complex forms. 

8. Nickel remarkably increases the useful properties of 
steel ; the result varying with the percentage as in Mn. The 
armor plates now (1891) preferred are made of nickel steel. 

9. Copper. When thoroughly deoxidized, steel may be 
improved by the addition of Cu, although it is thought by 
some that it makes steel hot-short, 

II. PHYSICAL CONSTITUTION. 

1. Homogeneity. 

As in chemical composition, no fused metal is naturally 
physically homogeneous, either in structure or in strain. 
These properties may be so modified by after-treatment that 
the following comparisons apply to non-forgeable metals as 
ordinarily cooled after fusion ; and to forgeable metals when 
annealed. This is the standard condition for their comparison* 

2. Structure. 

The structure is juaged of by the appearance of the frac- 
tures; for exact comparison these should be similarly pro- 



XV. — METALLURGY. 21 



duced. By varying the method of breaking it, the fracture 
of a bar of wrought iron may be made either crystalline or 
fibrous within a few inches of its length. 

Crystallization. It is assumed that ingot metals are crystal- 
line, and weld metals fibrous, although the ultimate crystal- 
line forms are doubtful.* Thus, the former may be supposed 
to consist of normal crystals, and the latter of distorted crys- 
tals cemented by a film of slag. 

Normal crystals are supposed to be formed like those of 
soluble salts ; the more slowly and quietly they are cooled 
from fusion, the larger and weaker they are, and conversely. 
(Bioxam, Art. 38.) 

The crystalline axes are found perpendicular to the cooling 
surfaces, so that surfaces of weakness are formed at the junc- 
tion of inclined systems. See figures 16, 17. For this reason 
the corresponding surfaces should be united by gradual curves 
so as to distribute strains which would otherwise be localized. 
Sharp re-entrant angles should be avoided in all structural 
masses, even the non-crystalline. 

Vesiculation. Another structural form arises from the oc- 
clusion of air and other gases during the casting. This causes 
^'' blow -holes,'' which increase with the viscidity of the fluid 
mass. On the other hand, when the metal is free from blow- 
holes, an axial cavity is formed, due to internal strain. This 
is known as 3. pipe. Figure 18. 

3. Strain. 

Differences in the rate of cooling throughout a fluid mass 
produce internal strain, the parts first solidifying being com- 
pressed by their adhesion to the layers cooling subsequently, 
which last are reciprocally extended. Similar effects follow 



* By some the primitive structure of ingot steel is supposed to be that 
of globules of the alloy imbedded in a mo e highly carbonized cement. 
This is called the Cellular Theory. 



22 XV. — METALLURGY. 

unequal heating. The importance of this principle is fre- 
quently apparent, particularly in dealing with iron castings. 

//. CAPACITY FOR RESISTING STRESS, 

Properties. 

Owing to the facility of referring other stresses to a tensile 
stress, this alone is generally considered, the incompressibiuty 
of cannon metals being sufficiently guaranteed by their com- 
bined hardness and tenacity. 

The principal properties of 1. tenacity, 2. elasticity, 3. 
ductility, and 4. toughness, have already been discussed. 

5. Hardness is properly the property of resisting penetra- 
tion ; combined with tenacity, with which it is almost invari- 
ably associated, it renders cannon metal incompressible by 
powder pressure, and in itself resists abrasion, erosion and 
impact from hostile shot. 

Steel may be artificially hardened by heating it, followed 
by its rapid cooling. Steel and bronze may also be hardened 
by their compression in a cold state ; externally by rolling 
and internally by mandreling, which consists in forcing 
through a hole conical plugs of slowly increasing diameter. 

It is noteworthy that by heating and rapid cooling, brass, 
bronze and the high Mn steel, p. 19, are softened, 

III, FACILITY FOR BEING WORKED, 

1. Fusibility. 

This diminishes the number of joints in a given structure, 
and, other things being equal, increases its cheapness, homo- 
geneity and strength. Recent advances in mechanical en- 
gineering have been principally due to the large units of con- 
struction afforded by the capacity and power of modern 
furnaces. Thus steel is replacing wrought iron, which is 
formed by agglutination. 



XV. — METALLURGY. 23 



2. Malleability, 

or to the power to endure hammering or roUing, particularly 
at high temperatures, enables metals to be forged into special 
shapes, thereby improving the quality of the metal and reduc- 
ing the labor of finishing. When combined with fusibility, 
it gives advantages peculiar to steel. 

3. Weldability, 

or the power of adhesion at high temperatures between 
masses is characteristic of wrought iron and low steel. It is 
upon this property that the manufacture of wrought iron 
depends. This property in construction is inferior to fusi- 
bility and hence is not utilized for steel except in small masses. 

The process of electric welding is now (1891) successfully 
employed. It consists in sending a powerful low-pressure 
current through the abutting surfaces of the pieces to be 
united. The resistance at the points of contact raises the 
neighboring metal to the temperature of incipient fusion; 
pressure being then applied, fresh surfaces are successively 
brought into contact. Owing to the high temperature of the 
first contacts, the current is mainly conveyed through the new 
ones and so on until a homogeneous joint is formed. 

Hollow projectiles are thus made from steel tubing welded 
to a point and a base. It is even proposed to heat finished 
pieces locally, so as to permit them to be bent or tempered 
without injury from the hammer or the fire. 

4. Annealability, 

or the power to become soft, facilitates reduction to size by 
cutting tools. All the cannon metals can be softened by 
annealing, but to steel only can the necessary hardness be 
restored, except mechanically. 

Grindi?ig. It fortunately happens that hardened steel, 
which can cut all the other useful metals, can itself be abraded 
by grinding almost as easily as when soft. 



24 XV. — METALLURGY. 



This permits the change of form which often follows hard- 
ening to be corrected by the use of either natural or artificial 
grindstones. See Chapter XVII, page 14 
CONCLUSION. 

The relative standing of the five cannon metals may be 
roughly indicated as follows : 

^STEEL-> , IRON > 

High, Low. Wrought, Cast. Bronze. 

1.1 f?l^„aS'/1 ^ ^ 3 4 5. 

t! 5 -( Homogeneity, I 1 o A. ^ f? 

2 % I Hardness, normal, f ^ ^ ^ d o. 

tn ^ 1^ Ductility, 4 3 15 2. 



f Fusibility, 3 4 — 3 

Malleability, 3 2 1 — 



O cJ 
cr 



C (U 

•^ § s( Weldability, — 2 1 



Annealability or ^ ^ o q 

variable hardness, f 

This indicates why bronze and the irons, which, owing to 
their workability, were until recently the only cannon metals, 
are now obsolete. 

IV. MANUFACTURE of the FERREOUS METALS. 

/. CAST IRON, 

Varieties. 

The gray pig is known diS foundry or 77ielting irow, the white 
pig as forge iron ; the latter is useful only for conversion 
into wrought iron. Mottled pig is an intermediate variety. 

Remelting. 

To obtain strong castings, the foundry pig is ordinarily 
remelted and run into molds of the required shape. 

The specific gravity of pig-iron is about 7.00, and its 
tenacity about 16,000 pounds to the square inch, but, when 
remelted, the specific gravity is increased to about 7.25, and 
the tenacity about doubled. 

The remelting is effected in cupola or reverberatory fur- 
naces, according to the kind of fuel available and the size 
and quality of the casting required. It is always necessary 



XV. — METALLURGY. 25 



to melt as quickly as possible, and with the least consump- 
tion of fuel. This usually requires artificial blast. 

In Cupolas. The cupola furnace is generally employed ; 
its size depends upon the amount of metal to be melted at a 
time, and upon the kind of fuel. 

A cupola extensively used is of the Mackenzie pattern, fig- 
ure 19. It consists of the iody B, of elliptical cross section, 
made of thick sheet-iron lined with fire-brick ; this is sur- 
mounted by a conical hood H, terminating in the chimney C. 
The blast is admitted through an annular tuyere extending 
around the bottom part of the furnace. The charge is intro- 
duced at the door D, and the molten metal, accumulated in 
the hearth H, is drawn off at the spout S, and carried to the 
mold through a channel or by means of ladles. 

The elliptical section of the body in combination with the 
annular tuyere increases the capacity of the furnace for a 
given intensity of blast ; the object being to maintain a high 
temperature in the vertical plane containing the transverse 
axis of the ellipse, along which, for regularity of feeding, it 
is desirable to cause the contents of the furnace to descend. I 

The cupola furnace saves fuel, labor and time, and fur- 
nishes a continuous supply of iron, which, since the carbon 
in the pig-iron is not diminished by melting, is liquid and 
therefore of the quality suited to foundry purposes. 

The charge consists of pig-iron and generally scraps of 
cast iron, a flux, and the fuel ; for the latter, coke and char- 
coal are best, though anthracite is generally employed. 

In Reverberatory Furnaces. Reverberatory furnaces are 
principally used for the production of large castings, and are 
specially adapted to all such as require great strength. Their 
use is sometimes necessitated if the fuel at disposal contains 
sulphur. 

The name is derived from the arch which beats back the 
flame on the metal to be heated. 

The furnace, figure 20, is built of fire-brick bound strongly 
together by iron bars or plates ; the hearih H is of refractory 



S6 XV. — METALLURGY. 



brick covered with a thick layer of Bre-sand ; the grate G is 
large, that a great volume of flame from the fuel may be 
drawn over the bridge -5 and through the furnace ; for this 
purpose the chimney C is made very tall when no artificial 
blast is used. The metal is introduced at the charging doors 
D, D\ and, when melted, is drawn off" at the tap-hole (h). 

The dimensions of the furnace depend chiefly on the charge 
of iron and quality of the fuel. They are of correct propor- 
tions if a nearly uniform temperature be produced in all parts 
of the furnace. 

Unlike the cupola, this furnace allows the iron to be kept 
liquid for any length of time ; and, as the fuel is not in con- 
tact with the metal, and carbon and silicon are removed by the 
air, a stronger iron results. On the other hand, it does not 
admit of constant casting, and involves a great loss of iron 
by oxidation ; owing to these circumstances and to the greater 
consumption of fuel, such furnaces are used only in large 
foundries, and, whenever practicable, are replaced by cupolas 
of large size. 

Properties of Iron for Castings. 

The color and texture of a casting depend greatly on its 
size, and on the rapidity with which it has been cooled, and 
upon its composition. As small castings cool quickly they 
are almost always white, and the surface of large castings 
partakes more of the quality of white iron than does the 
interior. 

When gray iron is melted, the particles of graphite to 
which its color is due are dissolved by the liquid iron, and if 
it be poured into a cold iron mold so as to solidify quickly, 
the exterior of the casting will present much of the hardness 
and appearance of white iron, the sudden cooling having pre- 
vented the separation of the graphite. This is particularly 
apt to follow the presence of manganese in the iron. 

At the instant of solidification gray iron expands more 
than white, giving a casting with sharp edges and a convex 



XV. — METALLURGY. ^? 



surface; and, as it subsequently contracts less, the initial 
strains due to cooling are less. 

White iron gives a casting with a concave surface, and 
mottled iron one with a plane surface, the edges slightly 
rounded. 

SPECIAL CAST IRONS. 

Malleable Cast Iron. 

By extracting a portion of the carbon from cast-iron its 
composition is assimilated to that of wrought iron and its 
toughness increased ; the result is known as malleable cast 
iron. 

The castings to be softened are packed with powdered 
haematite ore, or scales of oxide of iron, and the temperature 
raised gradually to a red heat ; this is continued from three to 
five days according to the thickness of the layer of malleable 
metal required. 

When withdrawn from the furnace, articles so heated have 
the appearance of ordinary malleable iron, but are lighter 
in color ; their fractured surfaces are white and finely granular, 
occasionally having a silky appearance like that exhibited by 
soft steel. 

The principal application of this process is to such articles 
as buckles, bits, stirrups, keys, etc. 

Case-hardening. The stratum of malleable metal on the sur- 
face may be converted into steel by the process of case-hard- 
ening, which consists in a similar heating in contact with ani- 
mal charcoal, after which, while still hot, the casting is plunged 
into water or oil. This process is applied also to articles of 
wrought iron, such as the parts of small-arms in which it is 
desired to have a tough, somewhat soft interior protected 
from friction or blows by a hard surface. The hammer and 
breech-block of the Springfield rifle are so treated. 



28 XV.— METALLURGY. 



SPECIAL ALLOYS. 

Varieties. 

Spiegeleisen or Spiegel {Sp) and Ferro- Manganese (FM) 
may be regarded as varieties of white cast iron alloyed with 
a varying proportion of Mn, That which contains over 20 
per cent, of Mn is known as FM. When Mn amounts to 
80 or 90 per cent., it may consume by spontaneous oxidation. 

The price of FM increases with its richness in Mn, for this 
limits the choice of ores and increases the temperature of 
reduction and fusion, and the loss by volatilization and oxi- 
dation. 

Silicon- Spiegel and Ferro-Silican are similar alloys, but con- 
tain much more Silicon. 

The following table exhibits roughly the ingredients of 
some of the principal special alloys, and illustrates the state- 
ments previously made as to the effects of Mn and Si upon 
the proportion of iron in combination. 

Note the gain in C as Mn increases, and its loss as Si 
increases. 

TABLE. 

Name. 8% Mn C Fe^ 

(combined.) etc. 

1. Ferro-Manganese, 80 7 13 

2. " '* 60 6 34 

3. Spiegel-Eisen, 1 10 5 84 

4. Silico-Spiegel, 10 20 2 68 

5. Ferro-Sihcon, 10 2 88 

Use. / 

These alloys are manufactured principally for the steel 
makers, being used by them to improve the quality of steel 
while in a state of fusion. 

Generally speaking, Ferro-Manganese is used when the 
quantity of C necessary is small as compared with the Mn 
required ; and conversely with Spiegel-Eisen, although in the 



XV. METALLURGY. 29 



latter case C may be added directly in a pulverulent form, or 
in a pure pig iron. 

The Silicon irons are principally used to prevent vesicula- 
tion; No. 4 is preferred to No. 5, as the increase in Mn 
causes the Si to more thoroughly combine with the steel and 
improves its structure. 

//. MODERN MANUFACTURE OF WROUGHT IRON. 

Principles. 

The great cost of the hand labor engaged in the ordinary 
process of puddling has led to the use of mechanical means 
for accomplishing this result. The two principal processes 
are those of Danks and Perfiot. Their common feature is 
the continuous rotation, by mechanical means, of the vessel 
containing the charge, thus avoiding the loss in time and 
power due to the reciprocating action of the puddler's rabble ; 
and diminishing the number of skilled workmen required. 

The principle involved in these processes is that given in 
Bloxam, Art. 219, viz.: That when cast iron is heated in con- 
tact with iron oxide, the C and Si in the iron take O mainly 
from the iron oxide in the fettling of the furnace. The C 
passes off as CO and CO^, and the Si as an iron silicate or slag. 
Danks Process. 

The furnace, Figure 22, consists of a horizontal drum, revolv- 
ing on rollers and lined with 2. fettling of lumps of haematite 
ore set in a fused paste of the same ore. The flame from a sta- 
tionary fireplace plays through one end of the drum and passes 
off through a movable flue at the other end. The removal of 
the flue permits the drum to be charged and emptied. 

For economy. the furnace maybe charged with melted iron, 
either directly from a blast furnace or from a cupola. If 
charged cold the rate of revolution is slow while melting; it 
is increased while boiling, during which the fettling and the 
flame rapidly oxidize the C and Si exposed by the rolling of 
the pasty mass and the adherent film and drip from that 



30 XV, — METALLURGY. 



which is melted. The drum is stopped to tap the cinder. It 
is then revolved more rapidly than before, draining the pasty- 
mass until it begins to ball. The large lumps, carried around 
by adhesion, fall on those at the bottom and help to work out 
the cinder. This is more thoroughly done afterward by the 
usual methods. 

Pernot Process. 

The pan revolves under a stationary cover, on an axis in- 
clined about 5° or 6° to the vertical, see figure 85. The fet- 
tling is thus exposed alternately to the flame and to the metal, 
the film of oxidized iron thus formed passing under the fluid 
mass and assisting the reduction. Balling still has to be done 
by hand ; but the process uses less coal than the ordinary 
one, and the furnace can be more easily repaired. 

These processes are losing their importance in consequence 
of the rapidity with which steel of various grades is supplant- 
ing wrought iron. 

///. MANUFACTURE OF STEEL. 
I. IN SMALL MASSES. 

1. Weld Steels. 

Puddled Steel. Puddled steel is made by stopping the pro- 
cess of puddling when the de-carbonization of the cast iron 
has sufficiently advanced. It is principally used for conver- 
sion into other kinds of steel. 

Blister Steel, which is made by cementation, being full of 
fissures and cavities, is fit only for a few rough purposes, as 
for facing hammers ; most of that made is used for conversion 
into other kinds of steel. 

Tilted Steel, When bars of blister steel are heated or 
hammered into bars under a tilt hammer^ Figure 40, the pro- 
duct is termed tilted steel ; spring steel is thus prepared. 

Shear Steel. Shear steel is produced by cutting bars of 
blister steel into convenient lengths, and piling, heating, and 
welding them under a hammer, whereby is obtained a bar of 



XV. METALLURGY. 31 

uniform quality known as single shear steel ; the quality of 
the metal is still further improved by a repetition of the pro- 
cess, forming a bar of double shear steel. The oftener the 
process is repeated, the more uniform is the resulting steel. 

Shear steel is capable of receiving a better edge and a 
higher polish than blister or spring steel; when well prepared, 
it is not much inferior to crucible steel. It is very exten- 
sively used in work where steel and iron have to be united by 
welding, as in axe-bits and scissors. 

2. Crucible Steel. 

Although blister steel by repeated working under the ham- 
mer acquires a tolerably homogeneous structure, it is still 
further improved by fusion. The process, invented a century 
ago, still remains in principle unaltered. Fragments of blis- 
ter steel are melted in crucibles, figure 23, covered to exclude 
the air, and the liquid poured into cast-iron ingot molds of 
the shape and size required. These ingots usually contain 
cavities; they are gotten rid of by heating the mass and ham- 
mering it into coijipact and homogeneous bars. 

Most crucible steel is now made direct from bars of the 
best wrought iron ; they are broken and placed in the cruci- 
ble with a small quantity of charcoal or pig iron, the amount 
varying according to the grade of steel required ; some alloy 
of manganese is subsequently added. The preliminary frac- 
ture of the material charged facilitates its classification and 
increases the uniformity of the product. 

Properties. 

In forging, crucible steel should never be raised beyond 
a certain temperature, varying inversely with the grade, 
or it will become brittle. It is difi&cult to weld, as it is usu- 
ally high in carbon. 

If a small quantity of manganese be added to the molten 
metal, the steel will be more forgeable and may be welded 
either to itself or to wrought iron. 



32 XV. — METALLURGY. 



Kemarks. 

The manufacture of the weld steels and of crucible steel is 
losing its importance, and crucibles are now principally used 
for small masses in which the desired quality of the product 
can, from the careful supervision exercised, be most easily 
maintained. 

The size of the crucible charge depends on the strength of 
the melter and rarely exceeds 80 lbs. ; but with well drilled 
men large numbers of such crucibles may be poured succes- 
sively into a common ingot mold of any size. Krupp so casts 
his large cannon, sometimes employing 1200 crucible bearers. 

II. IN LARGE MASSES. 

Processes. 

The principal processes are the Bessemer and various forms 
of the Open Hearth. Each of them has its province. The 
former, owing to its rapidity, excels in cheapness, although 
there is a loss of about 10 per cent, of iron ; the latter, owing 
to its controllability, excels in quality. This takes time and 
increases the cost by about 15 per cent., although there is in- 
cidentally a slight gain of iron. 

Carbonization and Tests. 

Owing to the loss of iron from oxidation when completely 
decarbonized, neither process is carried to an extreme, some 
C being always left in the metal and its final percentage being 
regulated by adding Sp or FM. 

The percentage of C is judged of by the fracture ; by the 
appearance of the nick required to produce fracture ; and 
more carefully by a rapid color test, which consists in compar- 
ing the color of a solution of the metal in dilute HNOg with 
that of a standard solution. In the Bessemer process this in- 
formation is applied to the next succeeding heat ; and in the 
Open Hearth, as the operation is less hurried, to the heat itself. 

Temperature. 

The high temperature attained permits re-melting on the 
spot of the scrap accumulating in all steel works, which would 



3tV.— MEtALLURGV. 33 



otherwise be of little value. In the Bessemer process this is 
due to the oxidation of the Si in the pig ; in the Open Hearth 
to the Siemens regenerator, which increases the temperature 
cumulatively to a degree limited only by the refractoriness of 
the furnace linings and the tendency of the gases to disso- 
ciate. Thus, like many other inventions, the Open Hearth 
process had to wait for the parallel development of some in- 
significant art, i. e. that of the brickmaker. 

Cranes. 

The production of metal by both processes depends upon 
the facility of manoeuvring large masses. Of the various pat- 
terns of cranes used for this purpose. Sir Wm. Armstrong's 
hydraulic crane, or some modification of it, is especially valu- 
able in Bessemer practice. Its efficiency depends upon the 
arrangement of peculiar valves which unite at a central point 
called the ** pulpit" and which place the control of the whole 
plant in the hands of one man. 

For an Open Hearth plant, where frequently very heavy 
masses must be moved and where the operations need not be 
so rapidly performed, these cranes may be supplemented by 
power swinging cranes or replaced by a traveling crane cover- 
ing the whole building. The traveling crane consists of a 
horizontal beam the ends of which roll on raised parallel 
tracks. The weight hangs from a truck rolling on the beam 
and may thus be transported to any point of the included 
volume. This crane presents many advantages and is used 
when the construction of the plant permits. 

Casting Ingots. 

In both processes, the melted steel is run from the furnace 
into a ladle from which it is distributed by a crane into cast- 
iron ingot molds. 

Casting is sometimes done through an independent iron 
gate entering the mold from below (Figure 24). The fluid 
metal should enter in a quiet, solid stream so as to avoid 



84 XV. — METALLURGY. 



entangling air. This is best done by emptying the ladle into 
the pool, from which it issues, mider a constant head, through 
a cylindrical nozzle. 

For gun work, the ingots are like Figure 25. The tong- 
hold serves to attach the porter-bar in forging ; and the drum, 
being girt with a sHng chain, permits the mass to be moved 
about and turned axially under the hammer. The dotted 
lines in Figure 25 indicate the form of the corresponding 
sections of the ingot. 

Ingots are cast at as low a temperature as possible consist- 
ent with fluidity in order to diminish internal strain and to 
save the inner surface of the mold, injuries to which may 
imprison the ingot. 

In order to fill the voids resulting from the shrinkage due 
to internal strains, castings of all kinds are generally sur- 
mounted by a smkifig head. This is a reservoir of the melted 
metal, the cooling of which is often retarded by containing it 
in a relatively non-conducting mold. 

For economy of fuel it is generally sought to forge the in- 
gots as soon as possible after they have solidified throughout ; 
but, owing to interruptions in the work, the sequence cannot 
always be maintained. Ingots may thus require re-heating ; 
this should be gradual so as to avoid internal strain. 

Fluid Compression. 

Whitworth's method of fluid compression tends to obliter- 
erate cavities by an hydraulic pressure of about 40000 lbs. per 
square inch. A very strong steel mold provided with a por- 
ous lining is employed. The pressure crushes down the vesic- 
ulated shell first formed next to the walls of the mold, and 
drives the fluid metal throughout the interstices. The lining 
allows the escape of gas. By this means the ingot is reduced 
about one eighth in length while cooling after casting. The 
best results, however, are thought to be obtained by careful 
melting and after-treatment of the steel while in a fluid state. 



XV. — METALLURGY. 35 



Bessemer Process. 

(Figures 27—30.) 

Varieties. 

There are two general processes depending on the nature 
of the pig-iron converted. If free from P, silicious or acid 
linings may be used ; but if it contains much P, basic linings 
are required. The former process, which is the more com- 
mon, is here described. 

Metal. 

The iron must contain Si as a fuel, and hence gray pig, the 
color of which is due to the carbon displaced, page 18, is 
used. It should be free from P and S, as they are not re- 
moved but, owing to the inevitable loss of iron, their propor- 
tion is increased. 

Main Operation. 

The pigs are usually melted in a cupola and the fluid 
charge, after weighing, run into the converter. A blast of 
air is then blown down through one trunnion and up through 
the perforated bottom and the fluid metal. The reactions 
resemble those of puddling* and are principally due to the 
heat evolved by the burning Si. This burns out the Mn and 
C in the metal and, by forming ferreous slags, removes part of 
the iron also. The fluidity of the metal is due to the inten- 
sity of the heat ; the latter is due to the rapidity of the reac- 
tion consequent upon the state of subdivision of the mass. 
The burning Si raises the temperature and promotes the 
fluidity of the bath more than does the C, because the CO 
formed absorbs much heat by expansion and carries it off; 
the slag remains and protects the bath from cooling. The 
small portion of Mn present also acts as a fuel. 

The basic process requires the blast of the Bessemer blower 



* It has been said as an example of mechanical progress, that we 
have replaced the laborious operation of the puUdler's rabHc by piercing 
the iDolten metal by invigjble bars of air. 



?56 XV.— METALLURGY. 

to be prolonged after the C and Si in the pig have been re- 
moved, the burning P maintaining the fluidity of the metal. 

Periods. 

Three periods are recognized, lasting as follows : 

I. Three to five minutes, Si burning. The free C in the 
pig becomes combined, in which state it is most easily oxi- 
dized. The flame is feeble, with a hissing noise. 

II. Six to ten minutes. The oxidation of C, principally 
to CO, makes the mass boil with a thundering noise. A 
yellow flame of incandescent particles is emitted at the nozzle. 

III. Four to five minutes. The flame, principally of N, is 
smaller, and of a pale bluish tint. In about 15 or 18 min- 
utes from the beginning, the flame suddenly drops, showing 
that the C is almost entirely gone. To save loss of iron by 
further oxidation, the blow is then stopped as the converter is 
turned down ; the carbonizer is then added by weight. If 
Spiegel is used, it is melted in a separate cupola. 

Final Operations. 

The carbonizer preferred for low steel is FM, which, al- 
though more costly than Sp, contains less C in proportion to 
the Mn, so that enough Mn may be added to reduce the iron 
oxide, combine with free O, and impart to the steel its char- 
acteristic qualities without introducing enough C to make it 
unduly hard. The production of FM is one of the improve- 
ments for which this application of the process had to wait. 

After standing for a few minutes, the contents of the con- 
verter are poured into a ladle, the slag remaining in the vessel; 
the slag is then emptied and the vessel turned up for a fresh 
charge. 

Remarks. 

The melted pig may be conveyed directly from the blast fur- 
nace ; but this is not often done, as it prevents the prelimi- 
nary grading of the pigs by fracture. 

The process is principally applied to the manufacture of 



XV. — METALLURGY. 37 



rails, for which it is sufficiently exact. The quaHty of the 
product may be improved if time and waste are neglected and 
the process carefully watched through the spectroscope. 

The steps of the operation in the acid and the basic pro- 
cesses, showing the rates at which the solid products are 
oxidized and the proportions of the different gases succes- 
sively formed, are represented in figures 28, 29, 30. In each 
figure one scale is that of time in minutes from the beginning 
of the blow, and the other represents the corresponding per- 
centage of the special product in question. These diagrams 
are the result of experiment. 

/ Open-Hearth Process. 

Varieties. 

The hearth may be either of the stationary or of the rotary 
type. In both cases the advantages of the process depend 
upon the Siemens regenerative apparatus, which requires a 
gaseous fuel. 

The rotary hearth has the advantage of steam power and 
of facility in making the repairs which the intense heat due 
to the regenerative apparatus frequently requires. It is also 
better able to dephosphorize pig-iron. The principal objec- 
tion to it is the liability of derangement of the rotating 
machinery ; but this can be overcome. Its process is here- 
after described. 

Distinctions were formerly made between the "pig and 
ore " and the " pig and scrap " processes, depending upon 
whether the melted pig-iron is decarbonized by the iron oxide 
or diluted by the addition of scrap steel low in carbon. 
Such distinctions are no longer important, as the former pro- 
cess is generally employed. 

The Siemens furnace with either the stationary or the revolv- 
ing hearth is a mighty instrument for achieving various metal- 
lurgical ends. Accordingly, many combinations are made in 



88 XV. — METALLURGY. 



its employment, pig-iron, washed pig, ore, fluxes, and, par- 
ticularly for commercial products, scrap being added as 
required or convenient. 
Gaseous Fuel. 

Advantages: 1st. Controllability, by which either an oxi- 
dizing, reducing, or neutral flame can be uniformly obtained. 
2d. Economy. 3d. Cleanliness. 4th. The accuracy with 
which the low temperatures used in annealing ovens may be 
estimated by the eye, the gas having been temporarily cut off 
so as to obtain a background against which the true color of 
Uhe heated piece will appear. 

The gas may be natural or artificial. 

Crude petroleum is becoming largely used as a fuel. Being 
thrown into the furnace as a spray, it has many of the advan- 
tages of a gas. It is also converted into gas by the action 
of steam at a high temperature.* 

Siemens Gas Producer. 

This consists of a number of chambers united in groups of 
four around a common stack E, figure 31. The stacks unite 
in a common trunk which leads with a slightly downward 
inclination to the valve box B of the furnace, figures 33, 34. 
Each chamber is essentially a wedge-shaped funnel with one 
inclined side terminating at the bottom in a grate B on which 
the fuel is slowly burned. The CO^ formed, ascending 
through the incandescent mass, becomes 2C0, and, with 
other gases due to the partial distillation of the superin- 
cumbent fuel, passes through the flue D to the stack E and 
thence to the trunk, having in the trunk a slight excess over 
atmospheric pressure to prevent leakage inward. The increase 



* The oxygen in the H^ O combines with the carbon in the oil, forming 
CO, and decomposing the hydro-carbons into new compounds richer in 
H. The H derived from the steam combines with the new compounds, 
and makes them still lower in the paraffine series. (Bloxam, Art, 320.) 



XV. — METALLURGY. 39 



of density due to cooling causes a gradual flow along the 
trunk. The same effect can be obtained by using a blast 
which gives more, better and hotter gas from fewer producers 
burning poorer fuel than does the natural draft described. 

Almost any kind of fuel from gas coal to sawdust may be 
used, depending on the purpose in view. 

The charging hopper A and the poker hole Care stopped 
to prevent the escape of gas. 

. Siemens Stationary Furnace. 

(Figures32, 33, 34.) 

Hearth. 

This rests in a cast-iron basin T, beneath and around which 
air circulates. It is enclosed in a rectangular box-like fur- 
nace about 30 feet long, standing above the floor-line W, and 
provided with the charging door U, and the spout V iox tap- 
ping out the fluid charge. 

Regenerators. 

These are the essential parts of the apparatus and are 
applied to many purposes in which high temperatures are 
required. 

The regenerator consists of four fire-brick chambers of 
varying section, K; L ; M; iV, arranged in pairs. They 
are filled with a crib work of loosely stacked fire-brick. From 
each of the end chambers K^ JV, gas-flues S lead up into the 
furnace ; and from each chamber Z, M, three air-flues P and 
R lead up alongside the gas-flues to a point above their exit 
in the furnace. This arrangement protects the metal from 
oxidation ; and the roof, made higher than where reverbera- 
tion is sought, from erosion by the flame. 

Valves, 

The gas, air, and reversing valves are shown in vertical sec- 
tion (laid over a longitudinal section of the regenerators) in 
Figure 32 ; in plan (laid over a horizontal section of the main 



40 XV. — METALLURGY. 



flues) F, G; Jy H in Figure 34 ; and in cross section in 
Figure 33. 

Operation. 

Gas from the producers, regulated by the valve B, passes 
down over the reversing valve C ; this is set so as to direct 
the gas into the main flue F and the regenerator K, where it 
percolates through the mass of hot brickwork and thence 
passes at a high temperature into the furnace. Air is drawn 
through the regulating valve F over the reversing valve C , 
through the main flue G into the hot regenerator L and, 
passing up the flue /*, meets the hot gas as above described, 
affording progressive combustion with intense heat. 

After burning, the flame passes down the flues R^ S into 
the other pair of regenerators J/, N^ which absorb most of 
its heat. It then escapes through the main flues J, H under 
the two reversing valves, and into the chimney flue AA' . 

After about twenty minutes, K, L becoming cooler and M, 
N heated, C, C are reversed by the handles D, when the 
currents of gas and air are also reversed. The efl"ect of 
reversal is cumulative, since to the heat of combustion is 
added that which the gases absorb from the brickwork before 
combustion. As the brickwork becomes progressively hotter, 
the ultimate temperature attainable is independent of blast or 
draught and is limited only by the refractoriness of the furnace 
linings and the tendency of the gas to dissociate at high tem- 
peratures. 

Advantages. 

The principal advantages are the high and uniform tem- 
peratures attainable, with the other advantages due to the use 
of gaseous fuel. 

Employment. 

When the furnace has been brought up to a melting heat, 
the bottom is repaired with fire-sand and the charge thrown 



XV. — METALLURGY. 41 



in by hand. After melting, it is stirred with iron -bars and 
treated as hereafter described in the Rotary Hearth, 

Pernot Rotary Hearth. 

(Figure 35.) 

Hearth. 

This consists essentially of a circular wrought-iron ' ^ pan " 
lined with refractory material and mounted on conical rollers. 
These run on a circular trough-shaped track mounted on a 
carriage ; the latter rolls on two parallel rails on which it may 
be run into and out of the stationary furnace chamber. The 
pan is rotated by a circular-toothed rack beneath it gearing 
into a toothed wheel or by an endless screw driven by steam 
power. The pintle, which is hollow and contains a stream 
of water, is incHned at about 6°, so as to bring the highest 
portion of the hearth next to the door. In case of accident 
to the tapping hole, more than one is provided. 

The lining of the pan varies with the kind of work. For 
ordinary melting it is of refractory siUcious material; but 
where dephosphorization is sought by the Krupp process, the 
lining is basic, preferably of lumps of refractory magnetite 
set in a paste made of powdered haematite and iron scale. 
The lower courses of the roof are then of dolomite brick. 

Operation 

For steel making, the charge, consisting of about 15 tons 
of pig-iron free from P and 6", is thrown in through the charg- 
ing door while the pan is revolving ; this distributes it auto- 
matically. Further revolution of the pan then causes the 
unmelted metal to dip into and out of the bath as previously 
described for wrought iron. When the pig-iron is thoroughly 
melted, rotation is stopped and ore is added at intervals, 
each addition being followed by a violent ebullition of the 
bath. Samples of metal or ''spoon tests'* are taken from 
time to time and examined by the color test, the fracture, and 



42 XV. — METALLURGY. 



by the appearance of the nick made by the chisel at the 
fracture. When the C in the bath is low enough, Si and Mn 
are added to prevent vesiculation and to make the steel 
malleable. The process is continuous, taking about eight 
hours for a heat, with a variable interval for repairs. 

Bepairs. 

The hearth is repaired between heats by revolving it so as 
to bring the portions most cut by the flame under a hole in 
the roof through which material is thrown. The stationary 
portion is repaired at about every twenty heats, the pan being 
run out bodily on its carriage. This afl"ords a considerable 
advantage, since in repairing the stationary furnace, time must 
be taken to allow the mass of brickwork to cool down to an 
endurable temperature ; owing to the lack of ventilation this 
time may be very great. 



V. MECHANICAL TREATMENT OF STEEL. 

CASTING. 

The successful casting of steel into final forms is still un- 
certain. The principal difficulties arise from vesiculation and 
internal strain Steel castings frequently replace iron forg- 
ings of a low grade. 

ROLLING 

Rolling may be intended to produce forms either straight 
or circular, and may be performed either hot or cold. The 
latter has the special object of producing hard, polished sur- 
faces of exact dimensions and is applied to iron or steel of 
small sections only. The reduction is small. 

Hot Rolling— Straight. 

The following description of the rolHng of armor plate or 
of structural steel is taken as a type. 

The interior of a newly cast ingot is too liquid for safe 



XV. — METALLURGY. 43 



working, and by the time that this has sufficiently cooled in 
the air, the exterior has become too hard. Consequently, 
the cooling is often retarded in non-conducting soaking pits, 
in which the initial heat of the interior and that which be- 
comes sensible during solidification become uniformly dis- 
tributed throughout the mass. 

Or, if the ingot has become cold, it is brought slowly to 
the proper temperature in a heating furnace. If this is done 
too rapidly, the exterior may be over-heated before the interior 
is at the proper temperature. The principle involved is of 
wide application in the treatment of steel. 

The universal mill consists of two pairs of massive rolls at 
right angles to each other, so that one pair will roll the sides 
of the ingot while the other pair rolls its top and bottom. 
Each pair is driven by an independent steam engine. The 
direction of the rotation may be rapidly reversed, and the 
space between the members of each pair of rolls be rapidly 
adjusted to suit the varying dimensions of the work. 

A series of horizontal parallel rollers of small diameter, 
independently driven, convey the ingot to and from the rolls, 
and after rolling take it to the shears where it is trimmed and 
cut into lengths. 

These lengths, or blooms^ are often re-heated and re-rolled 
by a mill trai?i into various structural shapes. For small work 
the mill train usually consists of a series of rolls arranged in 
sets of three, one above the other, or three high. They con- 
tain grooves of appropriately decreasing section so that suc- 
cessive /^i^i'<fi' reduce the bloom to the shape required. The 
rotation of each roll is continuous, so that the piece passes 
in one direction above the middle roll, and in the opposite 
direction beneath it. 

In roUing large sections the two-high system is generally 
employed ; the rotation being reversed and the space adjusted 
at every pass. 



44 5tV.— MEtALLURGY. 



In all large forgings great care is taken to cut out all visible 
imperfections such as pulls^ which arise from deficient duc- 
tiHty in the metal, and cold shuts, whicli are due to the folding 
in of projecting portions at temperatures too low to admit of 
their union to the mass. 

Hot Rolling — Circular. 

A small cylindrical ingot is flattened out or " upset " into a 
"cheese" and punched from each side successively with a 
conical drift. The punchings, or pieces cut out, usually con- 
tain all the pipe. It is afterward hammered on the horn of 
an anvil, figure 37, until the approximate forjji is obtained. 
Then, being hung upon a fixed roller A, figure 38, another 
roller B, independently driven at a higher rate of speed, is 
raised by hydraulic pressure to the position shown by the 
dotted lines. The thickness of the hoop is thus diminished, 
and its diameter increased, since lateral spread is prevented 
by the flanges a b which come in contact, each with the end 
of the other roller. The process is used for making locomo- 
tive tires and short hoops for guns. It tends to give a fibrous 
structure to the steel, aff"ording great tangential strength. 

WIRE DRAWING. 

Operation. 

This resembles rolling, except that the conical aperture in 
the draw plate, figure 39, being stationary, the wire, previously 
pointed and lubricated, is drawn through it by power, gener- 
ally by being coiled around a revolving drum. Tubing is 
similarly made, but large sizes, like gun-barrels, are rolkd as 
described for rails, the sides being kept apart by an axial 
mandrel which is stationary. 

Effects. 

The effect of wire drawing at low temperatures resembles 
that of cold rolling in that it raises the elastic limit and tenacity 



XV. — METALLURGY. 45 



and diminishes the ductility of the metal so much that, if the 
original section is much reduced, frequent annealing is nec- 
essary. Steel wire has thus been given a tenacity of over 
333,000 lbs. per square inch with an elastic limit half as high. 
These qualities are especially adapted to the construction of 
" wire-wound" cannon. 

FORGING. 

This includes the operations by which hot metal is ham- 
mered into shape. It therefore requires furnaces, hammers 
and anvils. 

Furnaces. 

For large masses modifications of the Siemens fupnace 
called re-heating furnaces are now employed. These furnaces 
are frequently served by a curved crane of the form shown in 
figure 42. This increases the elasticity of the crane as against 
the shocks due to forging. 

Hammers. 

For light work hammers may be of the vibrating class known 
as //// or helve hammers, figure 40, in which a horizontal beam, 
working on trunnions, carries at one end a heavy head ; this 
is caused to rise and fall by the action of projections on a re- 
volving wheel. Or they may be of the class known as drop 
hammers, where a weight is raised by hand or by power and 
allowed to fall upon the work after the manner of a pile 
driver, figure 41. 

But for heavy work steam hammers are used. They are 
sometimes of the Single Acting type, figure 42, proposed by 
Nasmyth in 1833. The inverted cylinder is mounted on legs 
which spread sufficiently to allow freedom for the workmen. 
The cylinder is usually traversed vertically by a heavy 
piston-rod, to the lower end of which, sliding in guides 
attached to the frame, is fastened a heavy head or tup. 
Steam being admitted below the piston, it raises the hammer, 



46 XV. — METALLURGY. 



which is allowed to fall from any desired height. Its fall may- 
be arrested by choking the exhaust by the automatic opera- 
tion of the valves so that rapid rebounding blows may be 
struck. See figure 43 and page 54. 
Anvils. 

The anvil with its foundations constitutes one of the most 
expensive portions of a forge plant. The anvil of the 125- 
ton hammer at South Bethlehem, Pa., copied from that shown 
in figure 42, weighs about 1600 tons. 

In order to avoid the effects of vibration, the foundations 
of the anvil should be independent from those of the hammer. 

The anvil proper, like the tup, is generally flat, but both 
may be of various forms required by the shape of the work. 
Small work is thus produced with great exactness by being 
stamped between dies. The parts of small-arms and of other 
machines made in great quantities, such as those for sewing 
and for agricultural purposes, are thus very economically 
forged into very nearly their finished sizes. When of hori- 
zontally rectangular section, the anvil is generally set with one 
of its diagonals in the plane of the legs, so as to give room 
opposite all its faces for handling long forgings. Figure 43. 

The energy on impact being the same, the action of a heavy 
weight moving with a low velocity is preferred, as the efi"ect 
is more penetrating and less local. This principle is utilized 
in Condies hammer, in which, owing to the fact that the mass 
of the cylinder is necessarily greater than that of the piston- 
rod, the cylinder is made movable, the piston-rod being sta- 
tionary. 

The steam may be admitted above the piston, adding its 
pressure to the weight of the moving mass. Such hammers 
are Double Acting. 

For small work a single support, figure 43, gives sufficient 
steadiness and more room. The valve may then be worked 
by a treadle under the control of the smith so as to give him 
the use of both his hands. See figure 41. 



XV. METALLURGY. 47 



The local absorption of energy at the point of impact di- 
minishes the reaction of the anvil, so that, as the thickness 
of the work increases, the thoroughness of the forging dimin- 
ishes. This requires frequent rotation of the work so that all 
sides may be equally extended.* 

For this reason Ramsbottam's duplex hammer is used, the 
work lying between horizontal hammers moving with equal 
and reciprocal velocities. 

Anvils for hollow work. In forging hollow work, mandrels, 
which are heavy solid cylinders passed through the forging, 
are used in connection with the anvil proper. If supported 
throughout its length by a V-shaped notch in the anvil, the 
forging lymg in between, the mandrel is termed _/fj:^^/ if sup- 
ported only and directly at its ends, the mandrel is called 
swinging. Figures 44, 45. 

The effect of forging is greatly affected by the way in which 
the mandrel is used. Forging on a fixed mandrel extends 
the work in length but does not sensibly affect the internal 
diameter. Forging on a swinging mandrel increases both 
internal and external diameters without affecting the length 
of the work. Hence, the swinging mandrel is used for hoops 
which are too wide for the tire-rolling machine. 

Forging Press. 

The defects in steam hammers above referred to will prob- 
ably lead in time to a more general use of the hydraulic forging 
press designed by Whitworth, Figures 44, 45. Its principal 
advantage lies in the time during which the work is operated 
on; this permits the molecular flow desired. t 

* This is also true of rolling and limits the effective thickness of armor 
plates. 

t Opinions are divided as to the comparative merits of the hammer and 
the press. The advocates of the hammer prefer it on the following grounds : 

1. In forging solid work the effect of the hammer is greatest on the 
exterior which is retained; and least on the interior, which for cannon 
and heavy shafting is subsequently removed. The converse of this is 
attributed to the press. 



48 



XV. METALLURGY. 



VI. MOLECULAR TREATMENT OF STEEL. 

The quality of steel depends upon : 

1. Its composition. 

2. Its structure as modified by heating and cooling. 

1. Composition. 

Pure iron and carbon make a typical steel. But other ele- 
ments are of necessity present in all the steels met with in 
practice. 

Pure carbon steel is here discussed. 

2. Structure. 

Changes in structure from the effects of heating and quench- 
ing steel appear to be associated with changes in its density 
and also in the state of the contained carbon. What relation 
exists between the change in state of the carbon and the 
change in the structure of the steel is still uncertain. 

States of Carbo7i. 

Indeed, the precise nature of the states of the carbon, 
although much experimented upon and discussed, is not 
definitely known. As an indication of the uncertainty in 
this matter, and also of the idea which most theories contain, 
the following suppositions may be referred to. 

The carbon is supposed by Professor Abel to be either in 
the condition of an alloy, or of a diffused carbide. Another 
chemist calls it diamond, or dissolved carbon. Others, and 
the more recent authorities, waive this issue by calling it 
** hardening " or " cement" carbon. See page 18. 

Avoiding any specific hypothesis, we may designate these 
states respectively as Fixed or Free, The former name, as 

2. The prolonged contact with the dies of the press chills the forging, 
the initial temperature of which therefore must be excessive ; while the 
blows of the hammer are heating. 

3. Hammering exposes superficial defects while pressing conceals them. 
The 1 25-ton hammer, page 46, is intended for forging armor plates, 

the quality of the surface of which is most important. 



3tV.— METALLURGY. 49 



the preceding nomenclature would indicate, corresponds to 
the hard condition of steel, resembling that of white cast iron ; 
and the latter to its softer condition, resembling gray iron. 
See Bloxam, middle Art. 220. 

BrinelVs Experiments, 
Method. 

The accompanying diagrams, Figure 46, are principally 
based upon a long series of experiments made by a Swedish 
engineer, J. A. Brinell, upon the changes in the structure of 
steel due to heating it in diiferent temperatures and cooling it 
at different rates. His results appear to agree well with those 
of others. His method was : 

I. To heat separate bars of the same steel, but of varying 
structure, up to certain temperatures indicated by the color 
of the hot metal,* and then to cool them in one of two ways : 

1. Slowly in ashes, called herein cooling. 

2. Suddenly in cold water, called herein quenching. 

n. To examine a freshly fractured surface, the fracture 
being similarly produced in all cases. 

HI. To subject the steel after cooling or quenching to a 
chemical test as to the state of the carbon contained. 

Classification of Fractures. 

The recognition of fractures, like that of colors due to cer- 
tain temperatures, requires great experience, but the principal 
fractures may be designated by symbols, as follows ; 

Structure. Crystalline. Granular. 

i Coarse, A. D. 

Symbols. \ Intermediate, B. E. 

( Finest, C. F. 

Aspect, glistening, dull. 

The most important is F, which may be called amorphous^ 



*The irisated colors in figure 46 are the chameleon tints of the 
films of iron oxide of different thickness, which result when a 
polished steel surface is moderately heated. 



50 XV.— METALLURGY. 



the crystals or grains being invisible to the naked eye. The 
intermediate and various composite fractures described by 
Brinell are not noted herein. 

Characteristics of Fractures. 

A, B, C, are relatively soft. 
D, E, F, are relatively hard. 
A, D, have low density (open grain) and are weak. 
C, F, have high density (close grain) and are strong. 
Therefore, C has softness and strength ; it is extensible. 
This fracture is sought in annealing. 

Therefore, F has hardness and strength ; it is inextensible. 
This fracture is sought in hardening. 
F has the maximum density. 

DIAGRAMS. 

Explanation. 

Figure 46 illustrates the changes in structure and state due 
to heating and either cooling or quenching the steel experi- 
mented on by Brinell. The axis of each diagram intersects a 
common scale of temperatures which, for any particular grade 
of steel, are indicated by the accompanying colors. 

The temperature W is critical in its effects on structure and 
state : it is the only high temperature at which, without having 
been exceeded, if steel be que7iched, the resulting fracture will be 
amorphous, F. The lower the grade of steel, the higher is the 
temperature corresponding to F, and conversely. The cor- 
responding color must be determined empirically for each 
grade, and, for important work, even for each ingot of steel. 

The steel used by Brinell had about 0.50 per cent, carbon, 
such as is used for cannon. 

Each diagram represents a group of experiments upon bars 
in which the same structure had been previously produced by 
the methods indicated above. An ordinate along the axis 
represents the temperature to which a piece of steel was 
heated ; the abscissa to the left represents roughly the result- 



XV. — METALLURGY. 51 

ing coarseness of structure. The character of the structure is 
indicated by reference letters. The extremities of abscissae 
so determined are connected by a line indicating whether, 
after heating to the desired extent, the bars were quenched or 
cooled. 

'Quenching is represented by a full line . 

Cooling is represented by a wavy line'-^^_^'^,^_^'^.^^ . 

The dotted line to the right of the axis represents roughly 
by its abscissae the state of the carbon at different temperatures, 
its relative freedom being represented by the corresponding 
abscissae of the dotted hne. 

Interpretation. 

Study of the diagrams will show that — • 

At W quenching always gives F and fixes carbon. 

At W cooling always gives C and frees carbon. 

Below W the crystalline structure does not change. 

Below W the granular structure gradually becomes finer. 

Below W the amorphous structure gradually becomes 
coarser (the only change possible). 

Above W all structures gradually become coarser, being 
crystalline if cooled, and granular if quenched. 

The change of carbon from free to fixed is sudden and is 
called hardening. 

The change of carbon from fixed to free is gradual. If 
partial, it is called tempering, and if total, it is properly 
termed annealing. 

Crystalline structure is associated with free carbon. 

Granular structure is associated with fixed carbon. 

Conclusions as to the Treatment of Steel. 

1. After forging a cutting instrument or spring, it must be 
hardened so as to fix the carbon, as a necessary preliminary 
to its gradual release by tempering. 

2. In tempering hardened steel, the less it is heated the less 



52 XV. — METALLURGY. 



is its structure affected; and the less is the change in the 
state of the carbon. 

8. The fixed state is the more stable, so that it takes time 
to change it throughout the mass without exceeding the de- 
sired temperature externally. Such an excess would affect 
the structure of the over-heated parts. The metallurgical 
term soaking aptly illustrates the manner of heating steel 
from which the best results are obtained. 

The effects due to a given temperature may, however, be 
produced by exposing the steel to a lower temperature for a 
longer time than usual. Many of the following apparent 
exceptions to the general rules appear to depend upon the 
question of time. 

4. The carbon having been freed by slow heating, the rate 
of the cooHng below W is indifferent unless the mass of the 
piece be so great as to cause the structure to change from the 
prolonged action of its internal heat. 

5. If W be exceeded the effect on structure of hardening is 
lost, and the steel must be cooled below W and re-heated to 
W to refine it. 

Use of the Term, Temper. 

Much confusion has followed the loose use of the term 
temper. Besides being applied to the grade of steel, it is also 
commonly used to indicate hardening; whereas we see that — 

Hardening is produced by quenching at W and fixing the 
carbon. 

Tempering is a mitigation of the hardness above produced 
which follows from subsequently heating steel to some tem- 
perature below W, the proportion of the carbon thus freed 
depending on the temperature attained. Whether the steel 
should then be cooled or quenched depends upon the mass 
of the piece. It is usually quenched. 

Annealing properly consists in cooling at W so as to free 
all the carbon possible and to destroy the effects of harden- 



X'V. — METALLURGY. 58 



ing. But it is also a term commonly applied to the cooling 
below W of steel, whether previously fully hardened or not. 
According to the temperature attained and to the time taken 
to cool the piece, it is softened and freed from internal 
strain. 

Bate of Cooling. 

The brittleness and the hardness of steel will be increased 
by increasing the rate of cooling from W, either by quench- 
ing in mercury, or in water the conductivity of which has 
been increased by acidulation or by the solution of a salt. 
The same effect is obtained by using water at a low temper- 
ature, or by frequent changes of the particles in contact, by 
motion either of the metal or of the water. 

By reducing the rate of cooling as by the use of oil or 
tallow, the effect known as oil hardening is produced. Its 
effect is intermediate between C and F, and is probably largely 
mechanical, the sudden cooling of the external layers prevent- 
ing the expansion of the internal mass during subsequent 
attempts at crystallization. This limits the size of the crystals 
formed and increases the strength of the metal; but it pro- 
duces some internal strain which may be relieved by temper- 
ing at a low heat. The charred oil next to the surface, like 
the scale, tends to delay cooling. 

EFFECTS OF FORGING, 

Above W. 

Except when in small masses steel is generally heated above 
W in order to give it the plasticity required for forging. In 
this case the crystals are not supposed to be destroyed but to 
be softened and expanded by the heat. Having been further 
disturbed by the hammer, they are supposed on cooling to 
assume the sizes and shapes due to the temperature at which 
they have been worked, with intervals between the crystals 
depending on the treatment received. Free crystallization 
thus implies porosity and a diminished density, which is 
further diminished by heavy forging at a high heat. 



M XV. — METALLURGY. 



Owing to the tendency of the crystals to shde over their ad- 
jacent surfaces, a heavy blow may cause the fracture of over- 
heated steel. It may indeed fall to pieces in the fire. But, 
if such steel be lightly and rapidly hammered over its entire 
surface, the effect will resemble that due to agitating a crystal- 
lizing solution (Bloxam, Art. 38), m the reduction of the size 
of the crystals and in the increased strength of the material. 

This effect having been attained, further forging at a lower 
temperature tends to form the piece and to distribute locally 
any cavities which may exist. 

In forging gun work the ingot is reduced in thickness about 
one-half; the reduction being greatest for those portions of 
the gun that lie nearest to the bore. 

Wa/er Annealing. Owing to the difficulty of penetrating 
large masses of metal by the vibrations of the hammer, the 
greater part of the metal treated as above will be, when cooled, 
like A or B or a combination of both. When the size of the 
piece permits, one remedy proposed is to re-heat slowly to W, 
to quench so as to prevent free crystaUization, and, as soon 
as the temperature falls sufficiently below W, to remove the 
steel from the water and allow it to cool slowly in air. See 
Diagrams IV and V. The internal heat removes internal 
strain. Railway axles are thus treated, the process being 
called "water anneaUng." 

The structure of a steel casting may be improved by heat- 
ing it to W and cooling it slowly. 

Forging Below W. 

When the hammer is of sufficient power, the best effect will 
be attained by forging just below W. The crystals are sup- 
posed not to be much expanded by this heat ; but, being 
softened, they may be compacted so as to destroy the porosity 
due to free crystallization. This treatment gives the highest 
density attainable, viz., 8.0; the steel resists the file, has a 



XV. — METALLURGY. 6B 



waxy fracture, and yields a beautifully veined surface when 
etched.* This work requires hammers of great power when 
large masses are thus forged. 

The experience of all steel makers tends to show the ad- 
vantage of forging at as low a temperature as possible. Work- 
men incline to over- heat the steel so as to diminish their labor, 
— but this should be avoided. 

A very fine quality of steel wire made in England by Stubbs 
and much used for making drills and fine tools is said to be 
made by being forged between semi-cylindrical dies by a light 
"pony" trip-hammer running with very great rapidity. The 
temperature required is attained by the hammering. 

INTERNAL STRAINS. 

These arise from differences in the rate of cooling through- 
out the mass, being increased in large masses by the deficient 
conductivity of hot metals. It thus requires much experience 
to judge of the internal temperature from the appearance of 
the outside of the mass. 

These strains increase with the maximum temperature at- 
tained, being greatest in the ingot. 

They also increase with the area of cross section of the mass, 
so that it is well to defer the hardening until the pieces are as 
nearly as possible of their finished dimensions. 

Uneven forging produces "hammer strain" which is re- 
Heved by annealing. 

Difference in section causes differences in rate of cooling, 
so that it is well to quench the thicker portions of irregular 
masses first. 

Other things being equal, internal strain increases with the 
grade of steel. 



* This is probably the original Damascus steel, which has been imitated 
by the moderns by twisting together and welding wrought iron and steel 
as in shot-guns. 



56 XV. METALLURGY. 



VII. GUN CONSTRUCTION. 

I. BUILT-UP GUNS. 

The operations are substantially as follows : 

Casting Ingot. 

For forgings such as tubes and jackets the ingot is often 
cast square, as shown in Figure 25. For short pieces like 
hoops, it is sometimes cylindrical. In order to obtain solid 
metal and to free it from slag, sand and other impurities a 
given amount of the top and bottom of each ingot is cut off 
and discarded during the process of forging. 

The ingot is sometimes cast hollow. But this is objection- 
able, for it transfers the unsoundness found in the centre of a 
solid casting to the middle of the walls of the gun. 

Coring. 

The ingot may then be trepanned by a sort of cylindrical 
saw by which a solid core is removed. This rapidly removes 
the more porous portions of the ingot, which are in a more 
valuable form for minor purposes than the shavings from 
ordinary boring. This operation sometimes precedes and 
sometimes follows the forging, depending upon what tools the 
plant affords and also upon the size of the gun. 

Forging. 

For solid ingots the work is constantly rotated during 
forging by means of the porter-bar, which is a long handle 
clamped to the tong-hold. A sling chain around the drum 
forms a fulcrum. Man or steam power is used according to 
the size of the work. 

Cored tubes and jackets are forged on a fixed mandrel to 
approximately their finished dimensions. 

Blanks for hoops are cut off the ingot and upset, or hammered 
lengthwise into a cheese-like form. After punching they are 
treated as described page 44, or, instead of rolling, they are 



XV. — METALLURGY. 57 



forged on a mandrel. The choice of operations depends on 
the length of the hoop and the facilities available. 

After every operation the piece is carefully chipped by hand 
to remove/////?, seams and cold shuts. 

Treatment and Tests. 

The term treatment applies to the methods employed to 
affect the structure of steel, viz., annealings hardening and 
re-annealing. The sequence of the tests is important. 

The *' hammer strain" is relieved by annealing. Annealing 
also facilitates the reduction by cutting tools to the rough- 
finished sizes required for oil-hardening. 

After annealing, tests of the metal are made to discover its 
characteristics, and thus, to a certain extent, to regulate its 
subsequent treatment. 

The pieces are then rough-bored and turned to nearly their 
finished size. 

They are afterwards oil-hardened (generally called "oil- 
tempered") by being uniformly heated to W in a furnace 
constructed with reference to the shape of the heated piece, 
e.g. tubes in a vertical flue, through many ports in the sides 
of which flame enters tangentially and hoops in an ordinary 
low furnace. Each piece is then immersed with its axis 
vertical in a large tank of oil, holding many tons. 

The tank is surrounded by a jacket through which a stream 
of water flows with required velocity. The oil is also caused 
to circulate by suitable arrangements. 

The pieces are re an?tealed * to remove the internal strain 
due to hardening. For this they are slowly heated to a low, 
red heat and allowed to cool very slowly. This heat improves 
the structure, but may slightly reduce the strength of the 
metal. 



* This is properly tempering. 



XV. — metallurgy; 



Tests of the metal are again made to see if it fulfils the 
necessary requirements. 

Assembling. 

The parts are then turned and bored to finished dimensions 
and assembled by shrinkage, the interior diameter of the out- 
side cylinder to be assembled being finish-bored to the diam- 
eter prescribed for the contact surface, and the exterior diam- 
eter of the surface upon which it is to be assembled being 
turned to the excess prescribed for the shrinkage. The eff"ect 
of the shrinkage, which follows the heating of the outer 
cylinder so that it may pass over the inner one, is sometimes 
to bring the surfaces in contact within the range of molecular 
cohesion. This phenomenon may sometimes be seen even 
between cold bodies. When the steel plugs, used to gauge 
the calibre of small-arms, being chemically clean, enter forci- 
bly a clean bore, they are sometimes lost through ''freezing." 

The hoops are secured by being screwed together, but 
preferably by interlocking projections that slip by each other 
when expanded by heat, figure 47. 

The policy of our government with regard to gun con- 
struction has been to obtain from private manufacturers the 
forgings rough-bored and turned, and to finish and assemble 
the various parts in its own shops. 

IL STEEL CAST GUNS. 

Objections. 

The economical advantages of this process, which consists 
in making the gun of a single steel casting after the manner 
formerly adopted for cast-iron guns, are off'set by the follow- 
ing objections: 

I. Mechanical. 

1. The enormous increase of the masses to be handled due 
to the weight of the sinking head, which, unless its functions 
can be replaced by other means, may weigh almost as much 
as the ingot itself. 



XV. — METALLURGY. 



A Steel-cast gun weighs, in the rough, about 3 times as 
much as the heaviest ingot required for a built-up gun of the 
same calibre. 

2. The difficulty of making molds strong enough to retain 
the high columns of metal required by modern powder. 

3. The loss in cutting up the sinking head, for re-melting 
or in disposing of failures. 

II. Constitutional. 

1. The vesiculation, impossible to correct by forging. 

2. The effect on crystallization due to slow cooling, also 
impossible to correct by forging. 

3. The segregation of elements of different densities in 
cooling. 

4. The internal strains developed in cooling castings which, 
for the heaviest guns, cast hollow, would possibly be 60 or 
80 feet high, with walls 3 or 4 feet thick. If cast solid, this 
thickness would be increased. 

Remark. This class of objections may possibly be over- 
come with increased experience in the treatment of the fluid 
metal, and by annealing the gun after casting. 

Such experience must be costly, for it can be acquired 
only by dealing with masses approximately as great as those 
of the guns themselves. 

III. Structural. 

1. The impossibility of making physical or chemical tests 
of internal specimens. 

2. The impossibility of adapting the composition of con- 
centric parts to their specific functions by the principle of 
*' Varying Elasticity," to be hereafter discussed. 

3. The neglect of the principle of "Initial Tension" by 
which the inner parts may, by preliminary compression, be 
prepared for the strain of extension on firing. This principle 
is ilhistrated when a blacksmith shrinks on a tire. 

IV. Historical. 

1. Krupp's original guns, which were massive forgings, 



CO XV. — METALLURGY*. 



have been gradually replaced by guns of increasing com- 
plexity of structure. 

2. The only recorded failures in built-up guns have occurred 
in the large masses constituting the tube ; sometimes when 
unsupported, as in the chase; or when imperfectly supported, 
as when a steel tube was surrounded by a jacket of ductile 
wrought iron. This, having been expanded beyond its elastic 
limit, failed to support the tube, which, on further firing, 
cracked. 



XVI. — PROJECTILES. 



CHAPTER XVI. 

PROJECTILES. 

Definition. 

Functionally speaking, a projectile is a vehicle for the 
transfer of energy to a disconnected object. 

The energy transferred may be wholly kinetic, as when 
the projectile acts by impact only. It may be wholly potential, 
as when the kinetic energy of the envelope of the mass may 
be neglected in comparison with the potential energy of its 
contents. And it may be of both kinds, as when the kinetic 
energy of the envelope is considerable. 

SECTIONAL DENSITY. 

On account of the work done on the intervening resist- 
ances, the energy actually transferred to the object will 
always be less than that originally imparted to the projectile. 

The resistance to penetration offered by the intervening 
medium and the object, other things being equal, varies 
directly with the area of cross-section, a^ at right angles 
to the trajectory. Let us call, d, the diameter of the circle 

whose area is, «, and F=f—- — the total resistance causing 

retardation. 

The retardation, which for a given projectile is propor- 
tional to the loss of energy per unit of path, will, for differ- 
ent projectiles meeting the same resistance, vary inversely 
with the mass of each projectile; or, calling; 



XVI. — PROJECTILES. 



p, the retardation in the direction of the axis of Xj 
M, the mass of the projectile; 
E, the energy in the direction of X; 
we have, neglecting variations in g; — 

_dE \ _gp7t d"^ _ d^ 

^~"d^"M~ ~T~ 'W^W* (-^^ 

in which k, is some function of the pressure per unit of area, 

/, which pressure will vary with the veloucity, the meridian 

section and the nature of <^he surface of the projectile.* 

d^ 
The ballistic coefficient^ or coefficient of retardation ^2,^ -— 

is called, may therefore be used to compare the inherent 

capacities of projectiles for retardation; and the reciprocal 

W 
of this expression, or —-^ which is called the j-^<r//^^/dr/^<?;zj/(>', 

may be used to compare their inherent capacities to over- 
come resistances. In English measures ^is taken in pounds, 
and d in inches. 

VARIATIONS IN SECTIONAL DENSITY. 

Causes. 

The sectional density of a projectile may be increased as 
follows: — 

I. If the dimensions are constant, by increasing the mean 
density. 

II . If its mean density is constant, by varying its dimen- 
sions, viz. : — 



* Since the form and dimensions of a projectile are independent of its 
velocity, and since the effect upon p of variations in the meridian section 
and the nature of the surface is small compared with those which result 
from changes in its diameter and weight, and disappears when similar 
projectiles are compared; we may for the present consider, k, for any pro- 
jectile as constant, so that the value of p may be considered to vary only 
With the relation between d^ and W% 



XVI. — PROJECTILES. 



1. If its proportions are constant, by increasing its calibre; 
since w varies as d^^ while a varies only as d}. 

2. If the calibre is constant, by increasing the weight. 

3. If the weight is constant, by decreasing the calibre. 
All these changes virtually lengthen the projectile. 

Effects on Flight. 

Increasing the sectional density of a projectile which has 
a given initial velocity increases its range and penetration, 
since the loss of energy over a given path is diminished. It 
may also increase its accuracy, since the time of flight over 
a given path, and therefore the effect of various perturbat- 
ing causes may be diminished. The penetration is still 
further increased by increasing the indeformability of the 
material of which the projectile is composed, so that the 
work of deformation on impact may be done rather by the 
projectile, than upon it. 

But, owing to the non-coincidence of the centers of mass 
and of the area exposed to the resistance of the air, 
during the flight of an oblong projectile a couple is formed 
which tends to cause the projectile to tumble or revolve 
about a transverse axis. This diminishes its sectional den- 
sity and makes it variable. Such projectiles are therefore 
given the rifle motion, which impresses upon them sufficient 
angular velocity about the longer axis to make this a stable 
axis of rotation, and therefore to make their sectional den- 
sity constant and a maximum. The same reason applies in 
a less degree to spherical projectiles, in which the centres 
of mass and of figure can rarely be made to coincide. 

Effect upon the Gun. 

Increasing the length of an oblong projectile increases 
its tendency to tumble, and hence requires a greater energy 
of rotation. This diminishes the kinetic energy of transla- 
tion due to the conversion of a given charge. In a certain 



XVI. — PROJECTILES. 



sea coast rifle the rotary energy amounts to about 0.01 of 
the total muzzle energy. 

Also, since increasing the sectional density increases the 
mass to be moved per unit of sectional area, a given accel- 
eration requires an increase in the intensity of the gaseous 
pressure per unit of area. Therefore, since V=/adt, to 
obtain a given initial velocity with a projectile of which the 
sectional density has been increased, the stress upon the 
gun must also be increased unless special provision be made 
by the methods indicated in Chapter XI. 

Owing to the weakness of cannon in use when the rifle 
principle was first applied, the increase in sectional density 
required a reduction in the initial velocity; this, although 
compensated for by greater accuracy and longer ranges, 
caused the initial portions of the trajectory to be more 
curved than with the spherical projectiles formerly em- 
ployed. See Chapter I. Consequently, the general adoption 
of oblong projectiles was delayed until the necessary im- 
provements in the gun and its ammunition had been per- 
fected. See Chapter XIII. 

Comparison of Forms. 

Although the oblong form is universally employed in new 
constructions, the following comparison illustrates some of 
the reasons influencing and opposing the change of form. 

Advantages of Oblong Projectiles, 

The form, capacity and sectional density may be altered 
indefinitely, with the advantages noted in the text. The 
following incidental advantages also exist: 

Projectiles of the same caliber, but of different natures, 
or mean densities, may be made of the same weight; so that 
they may be fired at the same ranges with the same angles 
of projection. 



XVI. — PROJECTILES. 



The oblorg form facilitates the operation of fuzes which 
act by impact; since the poinf-. and direction of the impact 
can be predicted. 

Disadvantages of Ohlofig Projectiles. 

The centers of mass and of pressure do not coincide; 
they are more expensive; the liability to injury of the soft 
metal device by which they are rotated requires greater 
care in their transportation and may interfere in their 
loading; in ricocheting over land or water their rebounds 
are much less certain and regular, both in altitude and 
direction. The rotation of rifled projectiles of the explosive 
class tends, upon bursting, to scatter their fragments unduly 
beyond the plane of the trajectory. The curvature of the 
trajectory at short ranges is increased. 

MATERIAL. 

The principle of sectional density mainly determines the 
selection of the proper material for a projectile, with regard 
to its behavior in the gun, in the air, and upon the object. 

Its application is so apparent that only a few of the minor 
properties of the materials employed will be mentioned. 

Stone was employed originally in catapults and continued 
to be used in cannon by the Turks as late as 1807. 

Lead is suitable for use against animate objects only, since 
in large cannon it is disfigured and even partially melted. 

Wrought Iron in large masses is expensive, as it requires 
welding and forging; it is also too soft. 

Cast Iron was until recently exclusively used for artillery 
projectiles on account of its fusibility and its small original 
cost. When cast in molds, so that the point cools in con- 
tact with a cast iron chill, while the body cools more slowly 
in sand, its local hardness, crushing strength and density 
are greatly increased, without causing brittleness in that 



XVI. — PROJECTILES. 



portion cooled in the sand. Against the wrought iron armor 
formerly employed, such projectiles are indeformable; but 
they are pulverized against the steel-faced and chilled iron 
armor of the present day. For ordinary purposes cast iron 
is still generally employed. 

Steel possesses all the qualities required in a projectile, 
but is costly. It is used in two forms, both of which are 
usually oil-tempered. 

1. Forged; including for special purposes, rolled or drawn 
steel tubes. This form of steel, especially when alloyed 
with chromium, is so far the best, but the most costly. A 
9 inch Whitworth forged steel shell, costing $100, or 12 
times as much as a similar projectile of chilled cast iron, has 
been fired three times through wrought iron 12 inches thick. 

2. Steel cast projectiles have, owing to their greater cheap- 
ness, been much experimented with; but, for the reasons 
given in Chapter XV, have so far proved inferior to those 
that are forged. 

SPHERICAL DENSITY. 

W 
Since the sectional density, -— , of similar projectiles in- 
creases with the caliber, if we divide the sectional density 

W 
by the caliber we shall obtain a constant, -73-, which expresses 

the weight per unit of volume of a cube whose weight is 
equal to that of the projectile and whose height is equal to 
the diameter of the bore. This is taken as the measure of 
the spherical density of the projectile. 

Since all spherical solid shot of the same material are simi- 
lar, their spherical density is constant, and may therefore be 
taken as the unit by which to measure the spherical density 
of oblong projectiles of the same material. 

Expressing the spherical density by S^ and the weight in 



XVI. — PROJECTILES. 



pounds of a unit of volume of the material by S, we have 
for a spherical solid shot, of which the volume is F, 



(7)'- 



ci^ d' ~3 \d J ~ 3 8* 

For projectiles made of iron, 6 may be taken as % pound, 
and 7t may be taken approximately as 3.0; therefore 

^., _ _ _ c, 

and for an oblong iron projectile in terms of S^^, 
^ _W' 1 _ 8 W 

S^i, therefore, expresses the effective increase in density 
that arises from elongating the projectile. 

We might proceed similarly with other materials having 
different values of 6; but it is convenient to retain iSg} as a 
common standard; so that, in general terms, S may be taken 
to measure the number of times that the mass of the inscribed 
solid iron sphere is contained in that of the projectile con- 
sidered. 

Unless the caliber be fixed, the spherical and sectional 
densities of projectiles vary independently of each other. 

The spherical density of the first oblong projectiles used in 
cannon in 1859, was about 2.0; but recent improvements in 
guns, powder and projectiles have increased it from about 3.0 
m 1880, to about 4.5 in 1887, the muzzle velocity not being 
correspondingly reduced. 

If all projectiles made of the same material had the same 
mean density and the same form, their spherical densities 
would be a function of their lengths. But as such is not the 
case, their length is independently stated, generally in cali- 
bers. In fact, the caliber is getting to be taken as the general 
unit of measure of all the linear dimensions relating to the 
interior of the piece. 



dim'B.t^' 



XVL — l^ROjECTtLEg. 



Corollary, 

Referring to the discussion on page 7, we see that the 
weight in pounds of a sohd spherical cast iron projectile is 
very nearly equal to the cube of its radius in inches. This 
affords an easy method of approximating to the weight of 
an oblong projectile when the type of gun from which it is 
to be fired is known. 

RIFLING. 

History. 

The invention of rifling by Gaspard Zoller of Vienna is 
said to have been made soon after the discovery of America. 
The first rifle grooves were made straight, and intended only 
to facilitate the loading of tightly fitting bullets. The advan- 
tages of the spiral groove, which were accidentally dis- 
covered, were not applied to oblong projectiles, even in small 
arms, until about 100 years ago, at which time the subject 
was thoroughly discussed by the eminent mathematician 
Eobins. It is worthy of remark that to Robins we owe the 
first practical apparatus for the measurement of the velocity 
of projectiles; a pendulum into which the projectile was fired, 
and from the nwDmentum of which that of the projectile 
could be computed. 

The general adoption of the rifle principle for small arms 
was retarded by the difliculty found in loading the rifle: this 
w^as generally accomiplished by the blows of a mallet on a stout 
iron ramrod. For cannon, attempts were made at an early 
date and are frequently renewed, to impart the rifle motion 
by the action of the gas, or of the air upon spiral grooves 
or wings formed upon the projectile. Except for low veloci- 
ties, all such experiments have failed to act with certainty, 
and the end has been attained only by the positive means 
mentioned in Chapter I. 



XVI. — PROJECTILES. 



Twist. 

The inclination of a rifle groove at any point is determined 
by the angle which its tangent at that point makes with the 
axis of the bore. Twist, is the term generally employed to 
express this inclination. 
Classification of Twists. 

When the inclination of the groove to the axis of the bore 
is constant, the twist is called Mniform. When it increases 
from the breech to the muzzle, the twist is increasing. 

Figure 1 shows the development of the surface of a bore 
rifled with uniform and increasing twists. Such curves are 
traced for the construction of templets, by which a combined 
motion of rotation and translation is given to the cutting tool 
of the rifling machine. 
Discussion. 

Let q) be the inclination of the groove at any point; and 
oa the angular velocity imparted to the projectile from being 
constrained to follow in the groove while moving in the 
direction of the axis with a velocity of translation v. Let r 
be the radius of the projectile. 

We may consider the velocity along the groove to be the 
resultant of two component velocities at right angles to each 
other; viz.: z; and f/ tan q). The latter imparts to a point 
on the surface of the projectile a tangential velocity 
r Go=^v tan cp. Hence, 

V 

CD =z tan cp • (2) 

That is to say that when the twist is uniform, the angular 
velocity increases only with the velocity of translation 
throughout the bore. When the twist is increasing, the 
angular velocity further increases from this cause; and other 
things being equal, it increases as the caliber diminishes. 

Since the muzzle velocity of a given projectile is fixed by 
independent considerations, the angular velocity at the 



10 XVT. — PROJECTILES. 

muzzle is measured by the tangent of the angle made at that 

point by the tangent to the groove and the axis. 

If / be the time required to make one revolution, and n 

be the length in calibers over which the projectile must pass 

in order to make one revolution, we have from Eq. (2), 

ODrt ^7tr 7t 
tan ^ = -— - = --— = -. (3) 

The twist is accordingly generally expressed in terms of n. 

It has been found that for ordinary artillery projectiles, 
about three calibers long, the requisite steadiness is given 
by imparting to the surface of the .projectile a tangential 
velocity of about 200 f. s. at the muzzle of the gun. Hence, 

7t V 

200 = r ci? = tan a>. F= - V .\ n—n — — . (4) 
n 200 ^ ' 

The value of n at the muzzle of the piece has generally 
been determined empirically as above indicated; a safe 
margin being allowed, smce no objection to a moderate in- 
crease in twist exists but that pertaining to a diminished 
energy of translation, and to the increased stress upon the 
piece. 

Recent analysis has determined the minimum twist at the 
muzzle for projectiles of varying proportions. 

It appears from this analysis that n is constant for similarly 
proportioned projectiles of the same material, whatever be 
the caliber; that it increases as the radius of gyration about 
the axis of revolution and the density of the projectile in- 
crease, and as the radius of gyration about an equatorial 
axis diminishes. Also, that the above value for the surface 
velocity is only approximate, since for the same projectile 
this may safely diminish as the initial velocity diminishes. 
Tangential Pressure on the Rotating Device. 

Since, for the same muzzle velocity of translation, the sta- 
bility of a given projectile depends only on the angular 
velocity which it has acquired at the muzzle; it appears that 



XVI. — PROJECTILES. 11 



SO far as this is concerned, it matters not whether the angular 
velocity be acquired only through or, the acceleration of 
translation, or through the combination of this cause with 
the gradually increasing twist. 

In the first case, the angular acceleration, will be greatest 
at first, when the gun and the rotating device are under 
their maximum strain, and will diminish as they become 
relatively stronger; thus making a disadvantageous distri- 
bution of the work of rotation, although the quantity of work 

W 
done will be constant and equal to -^ — /^/ w^ 

2g 

k, is taken as about 0.8 r in the linear units used for V, 

In order to make this stress, particularly that upon the 
rotating device, constant throughout the bore, so as to avoid 
either excess or deficiency in strength, the angular acceler- 
ation must be made constant. Herein lies the value of the 
increasing twist; since at the breech the diminished value 
of q) will compensate for the increased value of a\ and con- 
versely toward the muzzle. 

The determination of the precise form of the developed 
groove is difficult, both theoretically and practically, since 
the constancy of a depends upon the properties of the 
powder employed. 

It was thought for some time that a groove, the twist of 
which uniformly increased with the length of the bore, and 
having as its development a parabola, would give the best 
results. 

Recent practice indicates the advantage of employing a 

semi-cubic parabola, of the form x^—2py, which, in the 
case illustrated in figure 2, passes from a value of n=50 at 
the breech, to n=2D at the muzzle. Figure 2 shows how 
variously may be distributed the tangential pressures. To 
steady the projectile on leaving the bore, it has been thought 



12 XVI. — PROJECTILES. 



advisable to give to a short portion of the rifling neai the 
muzzle a uniform twist. 

MEANS OF ROTATION. 

I. MUZZLE-LOADERS. 

Classification. 

The first rifled pieces were muzzle-loaders, and hence the 
projectile was necessarily of smaller diameter than the bore. 
Rotation was imparted to it in two general ways: 

1. By making the rotating device fit the grooves before 
firing, by providing the projectile with suitable ribs or 
flanges. 

2. By making the device fit the grooves after firing by 
causing it to be expanded by the powder gases, after the 
manner of the gas check. Chapter VII. 

Operation. 

For this special purpose, and in all cases to avoid abrad- 
ing the grooves, the rotating device was made of a softer 
metal than the rest of the projectile; or, if formed on the 
body of the projectile, had given to it a large area of con- 
tact so as to accomplish the same result. 

Since the axis of such projectiles did not normally coin- 
cide with that of the bore, they could be centered^ or made 
concentric with the bore, only by chamfering the edge of 
the groove giving rotation, or by some similar device, the 
operation of which was uncertain. 
Comparison. 

Examples of the first class are shown in figures 3 and 4. 
Those with studs were until recently generally employed in 
Europe. The Whitworth projectile, the surface of which is 
a twisted prism, is a type of this class. It was once distin- 
guished, but is no longer employed in new constructions. 

The principal advantage of this class is that the projectiles 
are certain to take up the rifle motion. 



XVI.— PR0JECTIL1E5. 13 



They require special adjustment to the gun, both 
in manufacture and in loading; the escape through the 
windage erodes the bore; the stud holes weaken the projec- 
tile, and their arrangement in tiers, or the use of flanges 
renders it difficult to adapt these projectiles to the increas- 
ing twist. 

Examples of the second class are seen in figures 5, 6, 7. 

Their advantages are their adaptation to any gun of the 
proper caliber and the facility with which they can be load- 
ed, particularly in action. The former advantage led to 
their general employment during the Civil War, owing to 
the elasticity of the conditions then prevailing. Only the 
weight and the caliber of the projectile were fixed ; so that 
inventors were free to adopt many ingenious variations of the 
expanding principle. This is accordingly known as the 
American system. It answered well the demands of the 
situation but was uncertain in its operation; the expansion 
sometimes failing and the entrance of the powder gases be- 
tween the body of the projectile and the rotating device 
serving sometimes to tear this from its seat. See figure 7. 

The expanding cup has sometimes been applied to pro- 
jectiles of the first class so as to prevent the escape of gas 
above cited. 

Examples of Class II. 

The Butler and Eureka systems are the principal exam- 
ples of the second class retained for the muzzle-loading 
cannon still in service. 

The Butler System. Figure 5. 
The distinctive feature is the double lip formed in the 
expanding ring. The outside lip is expanded into the 
grooves, while the inner one is pressed against the tenon 
on the base of the projectile with an intensity proportional 
to that of the gaseous pressure. 



14 XVI.— PROJECTILES. 



The Eureka Projectile. Figure 6. 

The base of the projectile is a frustum of a cone in which 
the grooves, «, are cast. The expanding brass cup fits on 
the frustum and is prevented from turning by correspond- 
ing projections on its inner surface, and from falling off 
during transportation by the screw plug, b. 

On firing, the cup is forced forward and expanded into 
the grooves. 

II. BREECH-LOADERS. 

In breech-loading cannon the chamber is of larger diam- 
eter than the bore, and permits the use of a projectile pro- 
vided with a compressible device. 

Beside the advantages named in Chapter XI, the advan- 
tages of this class are certainty of action, better centering 
and the absence of windage. These qualities have caused 
their general- adoption to follow that of the cannon in 
which they are employed. 
History. 

Following the analogy of projectiles for small arms, it was 
at first attempted to coat them with lead, cast over the body 
of the projectile. But this was weak, the lead fouled the 
bore, was easily deformed, and added useless weight to the 
projectile when it was fired against armor. The length of 
the bearing prevented the use of the increasing twist, and 
the manner of applying the lead tended to alter the struc- 
ture of projectiles of hardened steel. Such were the pro- 
jectiles used by the Germans in the war of 1870. 

To overcome these objections, narrow rings or bands of 
copper, which is much stronger than lead, were placed in 
pairs at equal distances from the centre of gravity. Their 
diameter was equal to the caliber measured between the 
bottom of the grooves, or slightly greater, while that of the 
body was a little less than that between the lafids. Such 
projectiles required the uniform twist. 



XVI. — PROJECTILES. 16 



To this class belongs a projectile used in the small 
Hotchkiss cannon; figure 9. It has a thin sheet brass belt 
about one caliber wide, compressed radially into a shallow 
groove of equal width which is symmetrical with the center 
of gravity. The surface of the groove is circumferentially 
fluted, as seen in figure 9. When the piece is fired the 
powder gases press the band into the flutings, forming a 
series of rings, figure 10, which permit the metal to flow 
backward as the band takes the rifling. These bands are 
much cheaper to make and weaken the projectile less than 
the solid rings formerly employed in these projectiles. 
This ingenious method is confined to small calibers. 
Present Practice. 

The increasing twist now used in all large cannon re- 
quires a narrow bearing, which, to diminish the effect of the 
oblique action of the powder gases is situated in rear, at 
such a distance from the base of the projectile as to give 
sufficient shearing strength to that portion lying in rear of 
the band. 

To center the projectile a second band was formerly 
placed in front, but this has been replaced by a very slight 
enlargement of the body of the projectile near the base of 
the head. Figure 21. 
Position of the Eotating Band. 

Although, for ease in loading, the difference of diameter 
between the front bearing and the lands is made as small as 
is safe; unless certain precautions are taken, the oblique 
action of the powder gases — in a manner not thoroughly 
understood — may set up a nutatory or oscillating motion 
as the projectile travels through the bore. This leads to 
inaccuracy, reduces penetration, and may even leave the 
marks of the rifling on the front portion of the projectile. 

To diminish this effect, the front and rear bearings should 
be made the loci of conjugate axes of suspension and oscil- 



16 XVI. — PROJECTILES. 



lation. When the position of the front bearing is determined 
by the shape of the projectile, this can be accompHshed by 
swinging the projectile as a pendulum on a diameter of the 
front bearing, and ascertaining the time, /, of one vibration. 
Then the band should be placed at a distance from it, 

I = g l—\ since f=7t\/ — {Michie^ Eq. 404.) 

In order to diminish the effects of the oscillation in pro- 
jectiles in which, from unavoidable differences in manufac- 
ture, the method above described does not suffice, the width 
of the rotating band should be made as great as the nature 
of the twist permits. It is usually taken as about one-tenth 
of the caliber. 



LONGITUDINAL SECTION OF THE PROJECTILE 

Profile. 

The value of k in Eq. (1) depends largely upon the profile 
of the meridian section of the projectile and the nature of 
the surface. In the last respect breech-loading projectiles 
of the last class have a decided advantage over those of the 
first class of muzzle loading projectiles, since the atmocpheric 
friction is much less. This has required revision of the 
ballistic tables computed for the non-centered studded pro- 
jectiles for which these computations were originally made. 

The resistance of the air is not affected by the form of 
the extreme point, which, even if flat, is supposed to carry 
along with it a pointed core of compressed air; but the cur- 
vature of the head of the projectile is of great importance 
in that it affects the passage of the stream lines of air past 
the shoulder^ as is called the circle of tangency between the 
head and the cylindrical portion of the projectile. The cur- 
vature of the head is expressed by the length of the radius 
of curvature in calibers. This varies from 1.5 to 2.0 calibers. 



XVI. PROJECTILES. 17 



The form of the base is also of importance, in that, if also 
curved, it facilitates the flowing of the compressed air into 
the vacuum formed in rear of the projectile and so diminishes 
the difference of pressure upon the two extremities of the 
projectile ; to which difference the retardation is principally- 
due. Examples of this may be seen in the Whit worth pro- 
jectile and in the Hotchkiss projectile, already described. 
This advantage is not generally utilized, as it tends to diminish 
the sectional density, the strength of the base, and the facility 
of manufacture and of stowage. 
Mass. 

The mass of the projectile should be distributed so as to 
bring the center of air pressure as close as possible to the 
center of mass so as to diminish the overturning moment of 
the resistance of the air. This is a difficult matter, as the 
direction of the pressure is constantly changing; it is there- 
fore adjusted empirically by firing projectiles so weighted 
that the position of the center of mass may be varied 

INFLUENCE OF THE CALIBER. 

Following the principle of similitude by which cannon of 
the same class vary their linear dimensions in a given ratio 
to their calibers, it appears: — 

1. That the muzzle energy varies with the charge of 
powder, or as the cube of the caliber. 

2. That the capacity to convey this energy to a distance 
varies as the first power of the caliber. 

3. That the terminal energy varies as a power of the caliber 
which increases from about 3 at the muzzle to about 4 at the 
extreme range of the smaller of two pieces considered. 

STRUCTURE AND MODE OF OPERATION. 

Projectiles are classed according to their structure and 
mode of operation as follows : — 



18 



XVI. — PROJECTILES. 



1. Solid shot, or shot, 

2. Shells. 

3. Case shot. 

T. SHOT. 

Shot are used for penetration, generally of armor and in 
small arms against animate objects. For cannon they are 
confined almost wholly to the sea coast service. In order 
to diminish the effects of internal strain due to differences 
in the rate of cooling, shot are made not wholly solid but 
with an empty concentric cavity or core, figure 11. In such 
projectiles the point is carefully preserved. 

II. SHELLS. 

The increase in sectional density resultmg from making 
spherical projectiles solid, having been attained by a change 
of form, solid shot are now replaced by those which are 
hollow and whioh can therefore convey energy in a form 
unaffected by retardation. 

Shells are hollow projectiles containing an explosive and 
generally a fuze for its ignition at any desired point of the 
trajectory, The fuze may operate at a distance which is a 
function of the time of flight, when it is called a time fuze; 
or the explosion may result more directly from the arrival 
of the projectile at the point of impact. Such are called 
impact fuzes. Each class of fuzes, as will be seen, has its 
special province. 

The size of the cavity depends upon the specific function 
of the projectile. If this is intended to convey energy mainly 
in the kinetdc form, the smaller the cavity, the greater is the 
sectional density, and the more violent is the explosive 
required. If the energy is to be mainly potential, the larger 
the cavity the better the effect, provided that the resistance 
of the projectile to the shock of discharge is not unduly 
diminished. 



XVI. — PROJECTILES. 19 



The number ot pieces resulting from an explosion, and 
the facility with which the bursting charge wili" operate, in- 
crease with the brittleness of the material and with the 
completeness with which conversion occurs before rupture 
of the envelope occurs. Since for firing against troops frag- 
ments below about one ounce in weight are not considered 
dangerous, it is desirable to increase the number of fragments 
of about this weight as much as possible and so to compensate 
for the large, single mass formed by the base of the shell. 

The sectional density of the fragments approaches con- 
stancy and practically increases as they approach the spher- 
ical or cubical form ; therefore, many devices have been 
employed to regulate the rupture of such projectiles, as by 
making the walls double, figure 12 ; by giving to the cavity 
a polyhedral form ; or by grooving it spirally so as to dimin- 
ish the tendency to burst in a meridian plane. 

This appears from the following elementary analysis. 

Tet R and r, be the exterior and interior radii of a shell, 
the tenacity of which is T, supposed uniform throughout the 
section. Then, for the meridian rupture of a unit of length 
the necessary pressure will result from the equation — 

2r/ = 2(i?-r)r.-./=r('^-lY 

for an equatorial or transverse rupture we have 

Operation. 

The rupture of a shell will occur in one of the two ways 
above indicated only when the material is thin and inelastic, as 
in some shrapnel to be described. When, as is usually the 
case, the projectile has thick walls (Chap. V), the inner con- 
centric layers are more extended than those outside,they are fis- 
sured until fracture is determined by the line of least resistance, 



20 XVI.'— PROJECTILES. 



and the fragments are scattered by the energy remaining in 
the gases. The resistance of the envelope should therefore 
be kept within certain Hmits. 

Shells used against armor are pointed, and are filled and 
fuzed from the rear. They replace shot whenever possible 
since their penetration can be made almost as great, and 
their effects after penetrating the sides of a vessel are much 
more destructive both to men and machinery. 

Against masonry, shell serve a double purpose; first to 
penetrate the wall and fissure it by their explosion; and 
second, by throwing out the fragments to present a fresh 
surface for the next blow. 

Shells used against earthworks should contain the largest 
possible bursting charges. Such are called torpedo shells. 
They are sometimes made 6, and even 8 calibers long and, 
owing to the vertical angle at which they strike, are fired with 
low velocities from mortars and howitzers. 

A grenade is a form of shell, generally spherical, intended 
to be thrown by hand or to be rolled down a parapet against 
masses of troops making an assault. 

BURSTING CHARGES. 

Gnnpowder. 

When powder is used it is preferably of fine grain and of 
high gravimetric density. Such powder in firing, has a 
tendency to cake^ or become compressed into a mass of such 
density that the removal can be accomplished only by the 
chisel. This increases with the length of the charge and 
evidently tends to defeat its object. 

The caking, as indicated by the letters a, b, c, in figure 13, 
results from three causes; viz.: a, from the shock of dis- 
charge; b, from the rotation of the projectile, and <r, from 
the shock of impact. 



XVI.— PROJECTILES. 21 



The effect is to compress the powder and diminish its 
inflammability. If the impact be sufficiently resisted, the 
solidified mass may be thrown forward with such energy as 
to cause its ignition. To diminish caking, the cavity is 
often varnished; and to delay the explosion of armor piercing 
shell, the bursting charge is sometimes enveloped in flannel. 
On the other hand, where promptness is required, the French 
place loosely in the cavity a small wooden prism, figure 14, 
containing on two of its sides a network of oblique grooves 
through which the gases resulting from ignition may pene- 
trate the indurated mass. A slip of wood is tied over each 
grooved surface to prevent the channels from becoming 
choked. 

The bursting charge has been advantageously made of 
discs of concrete powder, strong enough to resist the causes 
leading to a and b, figure 13, but disintegrating under the 
influence of ignition. Such charges require to be filled 
through a hole, the size of which is objectionable. 
High Explosives. 

Gun-cotton is not injured by caking and, when specially 
prepared, does not readily explode on impact. This, or some 
equivalent high explosive, appears to be required for shells 
in which the excessive fragmentation of the envelope is not 
objectionable. This objection may be removed by using 
a small charge of dry gun-cotton in a shell filled with water. 

A high explosive is particularly required in armor piercing 
shells; these, if strong enough to penetrate the armor, may 
fail to burst with the utmost powder charge whrch they will 
contain or they may explode harmlessly before penetration 
is complete. 

The comparative insensibility of explosives of the Bellite 
class would seem to fit them particularly to this purpose; 
although the gx&dX force of gun-cotton makes it well adapted 
for use against earthworks. Its explosion is said to reduce 



22 XVI. — PROJECTILES. 



a large spherical zone of earth to a pulverulent form, by 
which its removal, and the exposure of the masonry which 
it is intended to protect, are facilitated. 

Sizft of Cavity. 

Great advantage has been found to result from increasing 
the size of the cavity by making the envelope of the shell 
of thin steel tubing. A 12 pound shell so made was found 
more effective against earthworks than a 50 pound shell of 
cast iron. To produce their full effect, such projectiles 
require an independent steel base, concave on its interior 
surface, so that it may be expanded against the walls instead 
of being driven outward by the explosion before the powder 
is entirely converted into gas. 



INCENDIARY PROJECTILES, 

Although the explosion of the bursting charge may suffice 
to ignite the splintered fragments of wooden structures, 
greater certainty in the effect results from filling the shell 
with an incendiary composition ignited by the discharge 
and flaming through specially constructed apertures in its 
walls. Such projectiles, called carcasses, and also red-hot 
shot, were formerly employed against wooden vessels. 

To this class may be referred light balls, thrown at short 
ranges to burn on the ground and illuminate the works of 
an enemy during a siege. To prevent their extincti*on, they 
were made to contain a loaded shell or a number of loaded 
pistol barrels. 

A more recent form consists of a shell containing a para- 
chute which is distended when the shell explodes, and, 
when carried over the enemy's works by the wind, illumi- 
nates them by the light of a mass of incendiary composition 
suspended beneath it. 

For modern warfare such devices are superseded by the 



XVI. PROJECTILES. 23 



electric light, projected from under cover by a reflecting 
surface. 

III. CASE SHOT. 

Where concentration of energy upon a given point, and, 
therefore, accuracy is required, shell, or preferably solid 
shot are used; but where, owing to the dispersion of the ob- 
jects and their inferior resistance the energy should be 
distributed, as in fowling pieces, case shot are employed. 

Case shot consist of a number of small projectiles, which 
we may call the cluster, contained in an envelope; according 
to the method of their liberation from which they are divided 
into two classes. 

1. Canister and grape shot, which separate at the muzzle 
of the piece in consequence of the shock of discharge. The 
general name, case, is now usually reserved for this variety. 

2. Shrapnel, which separate at a distance in consequence 
of the explosion of a small bursting charge, contained with- 
in the envelope. 

These projectiles forcibly illustrate the principle of sec- 
tional density in regard to the behavior of the projectile as 
a whole, and to the operation of the component parts, includ- 
ing the fragments of the envelope. 
Operation. 

The fragments separate in what is called the sheaf, or cone 
of dispersion, of which the mean trajectory constitutes the axis. 
Figure 15 shows a shrapnel provided with a time fuze, burst- 
ing in air; and figure 16 one with an impact fuze, bursting, 
as it is called, "on graze." 

The right section of this cone is circular and the horizontal 
section elliptical. The size and form of the ellipse for any 
section vary with the energies of the different component 
parts, horizontally in the plane of the trajectory and normally 
to that plane; and also with the sectional density of these 
parts. 



24: XVI. PROJECTILES. 

The inevitable lateral dispersion being sufficient for the 
necessary distribution, it is sought by various means to 
increase, at the moment of their separation, the component 
energy of the parts in the direction of the tangent to the 
trajectory. It is to the success of such efforts that the 
superiority of shrapnel over case shot of Class I is due. 

Case shot are generally employed against animate objects, 
a dangerous wound to which is taken to correspond to 
the energy required to pierce a pine board one inch thick. 
It is convenient to remember that this requires a velocity 
of about 500 f. s. in an ounce ball, or to an energy of about 
one eighth of a foot-ton. A velocity of 500 f. s. is accordingly 
taken as the limiting velocity for case shot. 

For reasons given, the fragments of the envelope are in- 
effective as compared with the members of the cluster, which 
are generally spherical. The envelope is therefore made as 
light as possible. 
Structure. 

But for the shock of firing, which deforms the members of 
the cluster even to the extent of consolidation, and which may 
even burst the envelope from the dilatation of its contents, the 
cluster would always be made of lead. But lead is expensive, 
and requires to be alloyed with tin or antimony; or to be im- 
bedded in a matrix as of sulphur or rosin; or to be packe'd 
in coal dust to resist this shock. Consequently, iron is used, 
except when the conditions require every structural advan- 
tage to be improved. 

Iron has the further advantage in certain cases of making 
the mean density of the case shot equal to that of the shell; 
this permits the firing to be regulated as stated page 4. 

The size of the balls depends upon the facility with which 
the envelope may be filled, upon the material of which they 
are made, and upon the distance at which, after separation, 
they are required to act. 



XVI. — PROJECTILES. - 25 



CLASS I. CANISTER AND GRAPE SHOT. 

These are distinguished by the lightness of the envelope, 
which is designed only for their transportation and loading. 
The balls, generally of cast iron, are now much smaller 
than before shrapnel attained its present importance. 

Canister. 

For smooth-bore cannon the envelope consisted of a tin 
case supported in rear by a disc which was designed to 
prevent the penetration of the gases into the cluster v^hile 
within the bore. To avoid the rotation of the projectile 
in rifled cannon, the envelope is stiffened so as to prevent 
its upsetting or dilatation into the rifling. In the English 
service this is done by inserting three trough-shaped pieces 
of sheet iron around the cluster. In the United States service 
a thin tube of malleable cast iron, closed at one end, is em- 
ployed. This is known as Sawyer's patent. The fragment- 
ation of this tube is assisted by spiral cuts. See figure 17. 

Since canister is retained only for the extreme simplicity 
of its operation at the short ranges at which it is employed 
by the defence, the size of the balls has been greatly 
diminished. 

When, as in the defence of the ditches of permanent works, 
the desired eflect is not complicated by requiring projectiles 
of different natures to be fired from the same gun, canister 
fire is replaced by that from machine guns. This is continu- 
ous and does not derange the aim so much. 

Grape Shot. 

These were formerly employed in smooth-bore guns 
against both animate objects and the masts and rigging of 
vessels. The iron balls were arranged in tiers of three, 
sustained by a central spindle, a top and bottom plate and 
two intermediate rings. Figure 18. In former times they 
were quilted into canvas bags, whence the name. 



26 XVI. — PROJECTILES. 



CLASS II. SHRAPNEL. 

Principles of Shrapnel. 
Notation. 

Let V be the initial velocity and v be the remaining ve- 
locity of the shrapnel at its explosion. 

Let Vy and v^^ estimated respectively at right angles to, and 
parallel to the tangent to the trajectory, be the mean veloci- 
ties of dispersion and of translation of the N balls that form 
the sheaf, irrespective of the velocities in these directions 
that are due to the remaining velocity v. 

The velocity v^^ which is taken without regard to its sign, 
may be due to either or both of two component velocities ; 
viz. : 1st. The velocity v^^^ due only to the bursting charge; 
and, 2d. In oblong projectiles, the velocity v^^^ due only to 
their rotation. 

The velocity v^ , which is an increment of the remaining 
velocity, is due only to the bursting charge, and its sign de- 
pends upon the position of the bursting charge within the 
projectile. 

Tet v' be the resultant velocity of translation due to z^± v^, 

Tet qp be the inclination to the surface of the ground of 
the tangent to the trajectory (the axis of the cone) at the 
point of explosion. It is important to remember that, as 
stated in Chapter I and to be proved in Chapter XX, the 
curvature of the trajectory, or the value of qp measured from 
the horizon, is a decreasing function of v. 

Let Q be the angle at the vertex of the cone of dispersion, 
figure 24. 

We will for simplicity suppose the cone to be composed of 
rectilinear elements, and the surface of the ground to be 
horizontal,* so that d will be the angle included between 



* For the effect of varying the inclination of the ground, see Chapter 
XXX, figure 34. 



XVI. — PROJECTILES. 27 

the upper and lower tangents to the sheaf at its vertex, 
figure 25. 

Distribution, t 

It is evident that the mean density of the sheaf will be a 

decreasing function of ^=2 tan-^ —L Also, from the horizon- 

tal projection in figure 24, that since — balls will be 

found in the area a b o d, the smaller is ^, or the more nearly 
does the cone approach a cylinder, the more uniformly will 
the balls be distributed over the entire ellipse a b o d. 

Also, the smaller the angle g), the greater is the eccen- 
tricity of the ellipse ; or, for a given lateral dispersion, the 
greater will be the dangerous space in the line of fire. 

N 
If a be the area of the ellipse, d= — will be the measure 

a 

of the density of the section ; this varies along the ellipse ; see 
figure 24. 

The shrapnel will be most effective when _ = — is the 

mean area occupied by one man projected on the ground 
by the elements of the cone. 

Besides ^, g) and N the value of a will depend on the 
height above the ground, and the distance in front of the 
target at which explosion occurs, or upon the distance vo=h, 

t Note. The curvature of the axis of the sheaf causes the section to be 
not truly elliptical, but oval as in figure 25. The ascent of the balls in 
the upper half of the sheaf, and the curvature of their trajectories due to 
their small sectional density, reduces their striking energy, so that those 
that fall near the large end of the oval are comparatively ineffective. 
This loss will be partly compensated for by the ricochet of balls nearer 
to the axis, provided they strike ground that is sufficiently hard. For 
ricochet, the angle of incidence shonld be less than 20° : this establishes 

a limiting value for g} -f" o <C^^°. 

These differences between the actual and the assumed conditions, hav- 
ing been understood, may, for this discussion, be neglected. 



28 XVI. — PROJECTILES. 



Nature of Target. 

The requisites of shrapnel vary somewhat with the dis- 
position of the troops against which it is to be used. These 
may be: 

I. Either in columns of manoeuvre, or in deep masses 
which it is the object of the artillery to force to deploy at 
long distances. In open ground these distances may uow be 
as great as two miles. 

II. Deployed in line at shorter ranges. 

In the first case, consistently with the limiting values of 

^j the values of 6 and /i should be small ; and conversely in 

the second case. In the first case, as the enemy will gene- 
rally be in motion, and therefore erect, cp also should be small ; 
and in the second case, as the enemy will generally be lying 
down and seeking cover, cp also should be large. 

These conflicting considerations require special treatment. 
In the first case guns with high velocities are needed, and in 
the second case the limit will probably be found in the use of 
field mortars. Between these limits guns may be used with 
reduced charges and at high elevations, and at the closest 
ranges, say within 300 yards, canister is most effective. 

The two cases correspond to the limiting cases of the cone. 
First, when = g) r= 0. Second, when 6 :=z cp =z 90"". 

The first case, being that most comprehensive and difficult 
to satisfy, and since it involves by its opposites the second 
case, is that herein discussed. 

Choice of Fuze. 

Shrapnel may be exploded in the two ways shown in fig- 
ure 16, viz., " on graze " by an automatic impact fuze, or in 
the air by an adjustable time fuze. These have different 
spheres of action as follows : 

Impact fuzes may be used at short ranges where v is large 



XVI. — PROJECTILES. 29 



and and cp are therefore small; and where q' the angle of 
reflexion (always greater than 9), is also small. Figure 16. 

But they act irregularly when the ground is soft or rolling ; 
and at long ranges when v is small and 9 is large, the energy 
lost on impact reduces the already diminished value of v, 
and consequently increases the value of 6, The time fuze 
is therefore essential for soft or rolling ground, and for long 
ranges over any ground. A possible objection to it applies 
to the risk attending its premature discharge when firing over 
friendly troops. 

On some accounts the time fuze is less well adapted for use 
at short ranges than is the impact fuze ; since for a given 
error in the time of its burning,* the greater is z', the greater 
will be the resulting variation in h, and therefore, for given 
values of 6 and qp, the greater will be the variation in a. 

Although this objection is partly neutralized by the small 
values of 6 and (jp at short ranges, the conditions seem to re- 
quire the use of two fuzes in each projectile. See the co7n- 
bination fiize^ Chapter XVIII. Meanwhile the improvement 
of the time fuze is one of the most important problems in 
ordnance. 

Computing the Value of d for Rifled Shrapnel. 

Let p be the mean radial distance of the balls. 

This is taken instead of the radial distance of the outer 
ball, as is generally done, since the distribution of the balls 
throughout the cross section of the sheaf is more important 
than their extreme lateral dispersion. 

Let r be the external radius of the shrapnel, taken equal 
to that of the bore of the gun. 

Although Fwil be reduced during flight, it is assumed, 
and experiment confirms the assumption, that at ordinary 



* The mean error (Chapter XXX, page 24) in the time of burning may 
be taken as about 0.05 sec. 



80 XVI. — PROJECTILES. 



ranges the angular velocity of the projectile does not sensibly 
diminish.* 

Under this assumption, from Equations (2) and (3) the tan- 
gential velocity of the mean ball will be nearly 

P" = ;~^. (5) 

and, since we are considering only the tangential velocity due 

to rotation, we have Vjy = p cj and 

6 p 0) pn F . -. 

tan - = '-J- = "^ ,. (6) 

If we substitute in this equation the empirical value of n in 
Equation (4) we have, 

tan-=-y--^, (7) 

and for a given shrapnel in which V^ n, and - are known, 

tan|=|; (8) 

an equation easily remembered, and which agrees fairly well 
with practice. 

History. 

The history of the improvement of shrapnel, which is now 
the principal field artillery projectile, illustrates many impor- 
tant principles. As stated, page 24, improvements liave 

tended to reduce the ratio -~- , and to increase the sectional 

7/ 

density of the projectile as a whole, and that of the balls it 
contains. 

Spherical Shrapnel, 

I. Shrapnel, as invented in 1808, by General Shrapnel of 
the British service, were simply spherical shell, loaded loosely 
with musket balls and a bursting charge. 



* Projectiles fired vertically upward have returned to the earth with 
sufiicient rotation to keep them point foremost. 



XVt. — PROJECTILES. SI 



In transportation the powder was triturated by the balls, 
and on firing the piece the shock might cause a premature 
explosion, or might conglomerate the balls ; sometimes even 
.causing the projectile to be ruptured by the resulting dilation 
of the cluster. The ignition of the bursting charge at the 
proper time was also uncertain. 

In order to make F large enough to give a large value to 
Z', the walls of the shell were made thick enough to stand a 
heavy propelling charge. But this diminished the value of 
N^ and, since the interstitial volume between the balls was 
large, 7u had to be made large in order to obtain sufficient 
pressure to burst the shell. The energy remaining in the 
powder gases after rupture of the walls being large, the balls 
were widely scattered, making 7>y large. The resultant value 

of vx was zero. At long ranges, tan - = -^ was there- 
fore large. 

2. The next step was the invention of spherical case, much 
used during our civil war. 

By imbedding the balls in melted sulphur and boring out a 
chamber for the bursting charge, figure 19, the value of iv 
could be decreased, and the certainty of its ignition at the 
proper time be increased. The matrix supported the walls in 
firing, so that their thickness could be decreased and N be 
increased. But the matrix often retained the balls after ex- 
plosion, and the value of 7^x was still zero. 

3. Colonel Boxer, of the Enghsh army, devised a shrap- 
nel, figure 20, in which the balls, hardened by an alloy of 
antimony, and packed in coal dust, were separated from the 
bursting charge by a wrought iron diaphragm around which 
the envelope was cast. The seat of the diaphragm and sev- 
eral other meridional grooves served to weaken the envelope 
and to diminish the value of w. 

While the projectile was necessarily fired with the fuze in 



32 XVI. — PROJECTILES. 



front, the non-coincidence of the centers of figure and of 
mass caused the resistance of the air to turn the Hghter 
portion of the projectile to the rear, so that z^x was always 
positive. 

This projectile marked the farthest advance of spherical 
shrapnel. 

Oblong Shrapnel. 

The advantages of the oblong form of shrapnel are as 
follows : 

It permits the base of the envelope to be strengthened 
without increasing the thickness of the walls. This, with im- 
provements in cannon and gunpowder, has increased the 
value of Vj and since the sectional density has been increased 
so that at long ranges ^ has been diminished, it has also in- 
creased the eccentricity of the section of the cone of disper- 
sion by the ground. By placing the bursting charge in rear, 
Z'x has become positive, and z'yb has become practically zero. 

An example of such a projectile is seen in figure 21, in 
which B^ is the cast iron body ; H, the ogival head of wood, 
covered with a sheet iron cap by which it is riveted to B ; 
C, the powder chamber, made conical to facilitate unloading; 
Z>, a disc by which the cluster is swept out to the front; T, a 
tube to carry the flame from the fuze, 7% to C. A paper lining 
keeps the rosin matrix from adhering to the walls of the cavity. 

The shght resistance of the attachments of the head makes 
of this projectile a sort of aerial gun. 

The objections to this projectile indicate the nature of re- 
cent improvements. The wooden head, the tube, the disc, 
and the thickness of the walls required by the nature of cast 
iron, diminish JV so much, that the balls form about one- 
quarter the weight of the whole projectile. 

The bursting charge is too small to produce sufficient 
smoke to indicate the explosion at distant ranges, and thereby 
to assist in correcting the aim. 



XVI. PROJECTILES. 



The position of the bursting charge is such that, while 
acting well in air, when used with an impact fuze the delay- 
caused by the passage of the flame through the tube causes 
the projectile to rise too high before bursting. 

Present Practice. 

The most recent ideas on the subject are embodied in 
figures 22, 23. 

Figure 22 contains a combined time and impact fuze. 

The bursting charge is situated in front, occupying the 
room which in figure 21 is wasted. It is large enough to 
give the smallest volume of smoke visible at extreme ranges. 

The envelope consists of a thin drawn steel tube, secured 
in rear to a separate base, and slit and compressed in front to 
an ogival form. 

The cluster consists of a column of leaden balls, separated 
by discs of cast iron. The discs are sunken to fit the balls, 
and form a skeleton matrix. 

When the bursting charge explodes, the slit ends of the 
point are thrown back, so as to dirhinish the sectional density 
of the envelope as compared with that of the cluster. 

The latter moves on with v' z=.v — v^ =v — about 200/. s. 

Figure 23 represents a more recent form, of which in 1891 
a number are in process of manufacture for experimental trial. 

Its construction is apparent. The tube is of thin brass, 
enlarging its capacity for powder, and facilitating the passage 
of the flame from the fuze. The w^alls are weakened by 
longitudinal grooves. It remains to be seen whether, com- 
pared with figure 22, the increase in 7'yb resulting from this 
construction will not neutralize the increase in Vyr^ , 

THE SEGMENT SHELL. 

An attempt was made some years ago to combine the 
functions of solid shot, shell and shrapnell in the segment 
shell, in which the cluster was composed of the sectors of 



S4 XVI. — PROJECTILES. 



concentric cylinders arranged so as to form a solid mass. 
But such a violation of the principle of the independe^ice of 
function^ which requires that where simplicity permits, eacli 
specific function be separately provided for, necessarily 
failed. The importance of this principle in the design of 
machines of all kinds can hardly be too forcibly stated. The 
opposite of this idea, that of combination, by which more 
than one office or function is expected of any one member 
of the machine or organization, is seldom found to be com- 
patible with the efficiency of the whole, as we shall have 
many opportunities of seeing during this course. The full 
development of the principle of the independence of function 
leads naturally to complication or the multiplication of parts; 
judgment is therefore required to compromise between sim- 
plicity and efficiency. The history of invention appears to 
indicate the pre-eminence of efficiency. 

As a case in point, it is now conceded that three types of 
the two classes of projectiles are required for field and siege 
artillery; viz.: shell, to convey kinetic energy for penetration, 
and potential energy for demolition and moral effect; and 
case shot for kinetic energy only. Although shrapnel, when 
reversed in the gun, may in an emergency replace canister; 
it is better to carry a few rounds of the latter, preferably, 
as in the British service, on the carriage which supports the 
piece. 

REGULATING SHRAPNEL FIRE. 

Referring to figure 24 we may consider the horizontal and 
vertical projections of //, viz., x — h cos cp ; j^ = A sin gi. 

Of these quantities, which are separately discussed in the 
regulation of fire, x is mainly varied by changing the time of 
burning ; and y by changing the angle of fire. 

Under given conditions x varies inversely as the range. 
Its variations, however, are not great, since there are com- 
pensations that tend to keep it constant. It is found that 



XVI. PROJECTILES. 35 



the best results follow a value of j\; = 50 yards for all dis- 
tances except those very short, for which x may increase up 
to 100 yards. If x be taken too small, too great a propor- 
tion of the shrapnel fired will explode beyond the target and 
be wholly lost. 

In order to utilize the small values of qp in the upper half 
of the sheaf, it is advisable to make y small. It is found 
that the best results follow a value of y varying from 2 yards 
at 500 yards range, to 6 yards at 2,500 yards range. Greater 
values of y are not used, since they are difficult to observe 
correctly at long distances. The reason for the increase of ji^ 
is due to the increase of cp at long ranges, and the consequent 
decrease in the area of the section cut from the cone by the 
surface of the ground. 

These rules are in the nature of approximations. In prac- 
tice the fire is regulated by signals from observers, placed as 
far as possible to the front and flank. 

EMPLOYMENT OF FIELD PROJECTILES. 

Shells. 

These projectiles when used with a time fuze would follow 
the principles laid down for shrapnel ; but the large value of 
6 and the small value of N would make this unprofitable. 

They accordingly use an impact fuze, which makes of them 
the best means of controlling elevations. See page 4, and 
Chapter XXX, page 20. 

They are generally used against inanimate objects to be 
demolished, pierced or set on fire. 

In the following cases they may be used against troops : 

1. At distances too great for the time fuze. 

2. When the enemy is hidden in a village, or in thick 
woods. 

The violence of their explosion assists their moral effect, 
particularly against horses and fugitive masses. 



36 XVI. PROJECTILES. 



Shrapnel. 

These are exclusively used against animate objects in the 
open, or in thin cover. They were found very destructive in 
the Russo-Turkish war. In siege oper ttions they serve to 
annoy parties working at night to repair the damages done 
by day. 

PENETRATION OF ARMOR. 
General Considerations. 

The penetration of armor depends principally — 

I. Upon the nature of the armor. In the order of resist- 
ance armor may be classed as follows : 

Cast iron with a chilled face, used only for land defenses 
and not considered herein. 

Steely forged and tempered. 

Compound^ viz., a wrought-iron back with a hard steel 
face. 

Wrought iron^ now obsolete. 

Roughly speaking, armor yields either by ptinching or 
racking. In the first case, as in wrought iron, the effect is 
local. In the second case, the energy of impact is distrib- 
uted throughout a greater mass of the plate and tends to 
crack the plate or to wrench it from its fastenings. The effect 
is mainly to remove an obstacle to further penetration. Cast 
iron armor yields in this way, and so do steel armor and the 
face of compound armor if too brittle. 

The object of the artillerist is to concentrate energy on a 
small area, so as to reach the objects which the armor is in- 
tended to protect, /. e., to punch. 

The object of ihe armor-maker is to protect these objects, 
by distributing the energy of impact as much as possible 
between the projectile and the mass of the plate, so that even 
at the risk of destroying the plate by racking, the shot must be 
kept out. 



XVI. — Projectiles. 87 



But if racking can be avoided without loss of resistance to 
punching, the quahty of the plate is improved. In the early- 
manufacture of armor, racking effects predominated ; these 
disappeared as its manufacture was improved ; while the resist- 
ance to punching was maintained or even increased. For ex- 
ample, the principal objection to steel, for armor as for other 
purposes, has been its brittleness. But at Annapolis, in 1890, 
carbon steel armor resisted punching, but was slightly racked. 
Nickel steel armor resisted both racking and punching. Com- 
pound armor failed in both respects. 

The nature of the backing or support against which the 
plate rests, considerably affects its resistance. Except for 
compound armor, for which the backing cannot be too rigid, 
the backing should be somewhat elastic, so as to absorb 
energy, after the manner of a cushion supporting a board in 
which one seeks to drive a nail. 

As the liability to racking increases, the number of the 
bolts by which the armor is held in place should also increase, 
so as to retain those portions which would otherwise be 
displaced. 

II. As a consequence of the above must be considered 
the resistance of the projectile to permanent deformation ; 
page 3. 

III. Upon the striking energy of the projectile, measured 
in a direction normal to the plate. 

Since the projectile acts after the manner of a punch, 
shearing its way through the plate, the energy is often 
estimated per unit of circumference. In earth and masonry, 
in which the material is soft, the projectile is supposed to 
compress it to the front, and the energy is taken per unit of 
area of cross section.^ 

* As experience with plates and projectiles of varying resistance to per- 
manent deformation, increases, such assumptions are gradually replaced 
by purel) empirical formulae suited to each special case. 



J^8 XVI.— PROJECTILES. 



Whereas in experimental tests normal impact is the rule, in 
firing at ships it will be the exception. The shape of the 
point of the projectile also tends to make it glance, so that 
for these reasons armored ships may be expected to resist 
more than the formulae predict. 

Haitian d's Formula of 1880.* 

The energy expended in other forms than in perforation, 
as in heating the plate and projectile, and in deforming the 
latter, has given rise to many empirical formulae, some of which 
may be found in the Course of Permanent Fortification. A 
very successful formula, Froloff''s^ assumes that -the energy so 
lost is proportional to the striking velocity, so that the pene- 
tration is proportional to the momentum of the projectile on 
impact. The following formula, which illustrates a principle 
already taught, is considered by recent writers to be one of 
the best Equation (15). 

Let t be the thickness in inches, of wrought iron armor that 
would just be perforated by a cast iron projectile, whose 
weight is W^ its normal velocity on impact v^ and its diam- 
eter d. 

Let e be the normal energy in foot-tons, or ^ = tt— s?r<7r 
^^ 2^^ 2240 . 

Let s be the energy in foot-tons per inch of circum- 
ference, or f = =- . 

TT a 

During a prolonged series of experiments made by Colonel 
Maitland it was found — 

1st. That / varied directly with £, or 

'=/(■?)■ « 

* It is inferred that the experiments on which Maitland's formula is 
based were made with ordinary cast iron projectiles, and that the armor 
was backed. 



XVI— I^ROJECTILES. 80 



2nd. It was also observed that when projectiles of different 
calibers were arranged in classes according to their spherical 
densities; in each class the penetration measured in calibers 
was very nearly proportional to the striking velocity. 

For a particular class, known as the standard projectiles, of 
which the spherical density was 3.0, the penetration was nearly 
one caliber for every thousand feet of striking velocity. This 
is known as Captain Orde-Browns *' rule of thumb." 

For purposes of comparison, let us assume a given gun to 
be fired against a given plate ; d and / will then be constant, 
and the variation in spherical density will result from varying 
the weight of the projectile. The variables will then be W 
and V. For the standard projectiles let these be represented 
by W, and v^, 

Owing to the number of experiments made with the stand- 
ard projectiles, special weight is given to the results obtained 
from them. These results are expressed in the following 
general formula, differing slightly from Orde-Brown's rule, 

viz. : « = ISOO - *^-^^- (^"> 

To pass from standard projectiles to those not standard, 
we use Equation (9) in order to ascertain the relation between 
V, and V, Under the hypothesis that d and / are constant it 

becomes v ^ f y\j ^ ' (11) 

Whence v\v\\ Jw : y/W„ or z; = v \/^. (12) 

In the standard projectiles, J^= 0.375 ^/^ ; whence, from 
Equation (11) ,, = 1^^^^W^ (13) 

Substituting in Equation (10) we have 



40 XVI. — PROJECTILES. 



Y/f__0.14; (14) 



"- 612.4 d 
Whence, multiplying both members by d^ 

'="'^= ski \/f-- 0.14^. (15) 

The value, /, thus obtained is the thickness of a plate that 
will just be perforated by a projectile having an ogival head 
with a radius of curvature of 1.5 calibers. If the radius of 
curvature is increased to 2 calibers, as is now customary, t 
will be increased by 5 or 10 per cent, and Orde-Brovvn's rule 
will increase in exactitude. 

If the plate resists perforation, then the penetration may 
be taken as about 0.9 of the estimated perforation. 

The Formulae of De Marre. 

The following formulae result from recent experiments in 
France and, except for Equation (20), cover a great range in 

calibers, and in the ratio - . 
d 

In the English units previously used we have for modern 

projectiles, viz., chilled iron shot and steel shells. 

I. For the perforation of wooden backing when used as 
such, i. e., not unprotected 

^b = 0.1823 / ^-^ ^ ••« (16) 

This is about 70 per cent greater than when the backing is 
unprotected. 

II. For a wrought iron armor plate that is hacked ; the 
resistance of the plate alone being considered 

^j = 5.809 /^-V-^ (17) 

Owing to the improvement of projectiles since 1880 this 
is less than the value implied by Equation (15). 



XVI. — PROJECTILES. 41 



For the entire target consisting ot the plate and backing 

^i = ^i + ^b. a8) 

III. For the rather soft steel plates^ generally used for heavy- 
armor, as made at Creusot, when backed 

^3 = 7.286 Z'-*^'-"* (19) 

See also Equation (18). 

IV. For the thin plates of hard steel, unbacked, used for gun 
shields, when attacked by the comparatively small cannon 
known as Rapid- Fire guns and Revolving Cannon 

^p = 12.86 /'-^^'-^ (20) 

These formulae, while abundantly verified in the French 
service, must be accepted with caution when the conditions 
differ from those under which they were deduced. 

Very's Formula. 

Mr. E. W. Very, formerly of the U. S. Navy, has recently 
proposed a means of comparing the resistance of steel plates 
that has long been desired, since it eliminates variables 
relating to the nature of the plate, its thickness and the cali- 
ber and velocity of the projectile, all of which may differ in 
experiments made at different times and places. 

It assumes that the projectile is not deformed, and that no 
other effect is produced but that of punching, which is sup- 
posed to be complete. The effect is referred to that pro- 
duced in wrought iron, since withm ordinary limits all such 
armor is homogeneous, and is therefore, well adapted for use 
as a standard of comparison. 

Suppose we find by trial that a certain projectile will just 
perforate a given steel or compound plate with a certain 
energy e^. Calculate the energy e^ required for the same pro- 
jectile to perforate a wrought iron plate of the same thickness, 

e 
and similarly backed. Then -1 z= g), m which qp is a factor 



42 XVI. — PROJECTILES. 



expressing the relative per cent of energy required to per- 

2140 
forate the steel plate, e, g. ^-— — 107 per cent. 

Since 1880 the improvement in projectiles has been so 
great that e^ has decreased considerably. Improvements in 
the quality of steel armor have increased e^, so that (p has in- 
creased from about 125 to over 150. See next topic. 

Weaver's Formula. 

It has long been thought that besides its thickness, the mass 
of the plate affects its resistance to penetration, and conse- 
quently the '■^ energy per ton of plate^'' is often recorded in the 
reports of firing against armor. No use is known to have 
been made of this knowledge, however, until the following 
formula, proposed by Lieut. Weaver of the U. S. Artillery. 

• It is probable that the work is practically confined to a 
mass of some definite volume immediately surrounding the 
point of impact, and that the volume of this mass is a cylin- 
der, the diameter of which is n times the diameter, d^ of the 
projectile, and the height of which is /, the thickness of the 
plate. 

Experiments show that a notable increase in temperature 
and the bulge are confined to a tolerably distinct ring, about 
2 calibers wide, so that n is probably not less than 5. It is 
probable also that it is safe to allow for an exterior ring which 
absorbs part of the energy, although the effects in this ring 
are not apparent. The value of 7i also depends upon the 
relation between t, the thickness of the plate, and d, the 
diameter of the projectile. Lieut. Weaver expresses this re- 
lation for Creusot steel by 

n = 6.25 + 0.22 (/ — d) (21) 

in which / and d are in inches. This value will depend upon 
the rigidity of the material, and is subject to correction by 
experiment. 



XVI. PROJECTILES. 43 



In wrought iron n will approach unity, as the effect is 
noticeably local and no great increase of temperature in the 
adjacent parts is observed. 

From a general consideration of records Lieutenant Weaver 
finds that about 1828 foot tons of energy per ton of plate is 
necessary to perforate the entire target, consisting of a steel 
armor plate and its backing. This assumes the plates to be 
substantially uniform in resistance, the projectile to be inde- 
formable, and neglects secondary effects, such as racking. 
Calling this coefficient, C ; the weiglit in tons of the disc in 
question, W^\ and the weight in tons of one cubic inch of 
the plate, w; he writes : 

£.= ff/,C=(«-'^)%/.^C (22) 

Supposing w — log ~^ 4.1028 and substituting for tt, w and 
C their values, we have the general formula 

A = 0.1828 ie d^ t (23) 

APPLICATION. 

We may now compare the foregoing formulae by reference 
to the experiments at Annapolis in September, 1890. The 
plates were 10.5 inches thick, backed by 36 inches of oak, 
and were fired at by steel shells, as follows : 

No. of fT- ■■ , TT^ Spher. Effect on 

shots. ^^^"^- '^ ^^ Dens. ^ ' Projectiles. 

8 Holtzer Steel, 6 in. 100 lbs. 3.70 2075 2988 6 unbroken. 

2 Firminy " 8 " 210 " 3.28 1850 4988 2 broken. 

Confining our attention to the unbroken 6 inch projectiles, 
only the points of which perforated the carbon and nickel 
steel plates, Lieutenant Weaver's formula gives ^g = 362 L 
If from this we subtract e^ = 77, per Equation (16), we have 
e^ = 3544, which is 18 per cent more energy than the plates 
received from any one blow. As the plates were not com ■ 
plete^ perforated, this would indicate that the value of 



44 XVI. — PROJECTILES. 



(p z= 195 from Equations (18, 21) is more nearly correct than 
that of (p = 158 assigned by Mr. Very's method ; viz., by 
dividing 2988 X 100 by the vaUie of c, = 1816, given by 
Equation (18). 

ROCKETS. 

Definition. 

A rocket is a projectile propelled by a source of energy 
which it contains ; it therefore performs also the functions of 
a cannon. 

Structure. 

A rocket consists of a cylindrical case of paper or metal, 
containing a composition formed of the ingredients of gun- 
powder mixed in suitable proportions. The front end of the 
case is usually closed, but the other end contains one or more 
holes or vents for the escape of gas from the ignited compo- 
sition. Within the rocket is a hollow space called the bore ; 
this may be formed by driving the composition around a 
spindle which is afterwards withdrawn ; or by boring out the 
composition after its compression to a solid state. 

The case is surmounted by a pointed head, which, for 
signal rockets, consists of a hollow paper cone, and for mil- 
itary rockets of any suitable projectile Depending upon 
the particular system of construction, some means is also 
provided for guiding the rocket in its flight. 

Composition. 
Since the composition is required to ignite readily, and 
since the amount of fouling is not objectionable, the pro- 
portion of sulphur is increased; and, since the gradual 
evolution of a large volume of gas rather than a large 
amount of heat is required, the proportion of nitre is dimin- 
ished, while that of charcoal is increased, so as to yield CO 
rather than CO,. To further delay the combustion the in- 
gredients are often mixed, rather than incorporated. 



XVI. — PROJECTILES. 45 



Bore. 

The bore is necessary to provide a large surface of initial 
combustion. In order to maintain a uniform pressure 
throughout the flight and so avoid either excessive strength 
and weight of the case when, at first, the pressure is low; 
or a deficiency of strength when, by the increase of the 
surface, the pressure increases, the composition should burn 
on a surface which is nearly uniform. 

To prevent its burning on a decreasing surface, the com- 
position must be so tightly packed within the case that the 
flame cannot pass around it. 

The conical form increases the initial surface without 
increasing either of the above objections. Jt also facilitates 
the withdrawal of the spindle and increases the strength of 
the composition at the section corresponding to the immov- 
able layer in a gun. Chapter VII, page 1. 

Vent. 

The momentum of the rocket is proportional to that of 
the escaping gas. The velocity of the gas will increase with 
the pressure, and this will increase as the size of the vent 
diminishes. The longitudinal and the cross sections of the 
vent must be so chosen that the gas will escape as fast as it is 
formed, or nearly so, otherwise the velocity of the rocket 
will be diminished and it may burst. See Chapter XI, 
page 8. 

The excess of the total pressure on the head of the bore 
over that on the base, and the diminishing mass of the 
composition accelerate the motion of the rocket until the 
resistance of the air is equal to the propelling pressure: the 
variation in velocity will then be slight. When the gas 
ceases to flow the rocket becomes an ordinary projectile. 

Guiding Principle. 

The propelling force of the gas acts always in the direc- 
tion of the axis of the bore; it follows, therefore, that with- 



46 XVI. — PROJECTILES. 

out some means of 'giving stability to this axis, the path 
described will be very irregular; so much so at times as to 
fold upon itself. Instances have been known when rockets 
have returned to the point from which they started. Stead- 
iness of flight is obtained either by a guide stick, or by 
rotation. 

The guide stick is used for signal rockets. It consists of 
a long wooden stick affixed to the case so as to bring the 
center of atmospheric pressure well in rear of the center 
of gravity. Any tendency to deflection is resisted by the 
atmospheric moment. 

The Hale rocket, figure 26, owes its stability to rotation 
produced by the escaping gas. As this expands on escaping 
through the vents, it presses against the concentric y^<?;?<r^i-, F^ 
partly surrounding each of the three vents, and so causes 
rotation. 

The effect is increased in Macdonald's Hale rocket by a 
similiar arrangement in front. In this rocket the bore 
extends throughout the composition. 
General Remarks. 

The difficulties found in constructing rockets so as to 
prevent the shrinking of the composition from the walls of 
its envelope; their inaccuracy, and their low capacity as 
vehicles of kinetic energy have limited their use m recent 
times to incendiary purposes, particularly in savage warfare. 
Where transportation is difficult and the enemy dwells in 
huts of an inflammable nature, as in Africa, the portability 
of these weapons causes them still to be retained by the 
British service. 

Rockets are also much used for transferring life-lines to 
the crews of wrecked vessels, and may be applied to the 
movement of floating torpedoes. 

Rockets are fired from inclined troughs or tubes. 

The 12 pounder rockets of the following named varieties, 



XVI. — PROJECTILES. 47 



fired at an angle of elevation of 8° 15', gave the following 
mean ranges and mean lateral errors (for the definition of 

these terms see Chapter XXX, page 24) : 

Range. Mean lat. error. 

Hale rocket 1312 yards. 37 yards. 

McDonald-Hale rocket... 2012 . " " 



XVII. — FABRICATION OF ARTILLERY PROJECTILES. 



CHAPTER XVII. 

FABRICATION OF ARTILLERY PRO- 
JECTILES. 

The fabrication of projectiles involves reference to the 
principles of founding, some knowledge of which is neces- 
sary to a practical education. 

Founding, or as it is less properly called, castmg, may be 
divided into three parts, viz.: 

I. Molding : by which a cavity, or ??wldj is formed to re- 
ceive the molten metal; II. Melting; III. Pouring. 

I. MOLDING. 
Material of Mold. 

Metallic. 

When the metal to be cast is fusible at a low temperature, 
so that it will remain liquid for some time after contact with 
a metallic surface, the mold may be made of a less fusible 
metal. This permits great exactness in the resulting casting, 
particularly if the metal does not contract much in cooling, 
and it allows the mold to be repeatedly employed." For 
such reasons the molds formerly used for making bullets, 
and those now employed for making fuze-cases of pewter, 
and for printing-type, are metallic. 

Metallic molds are also used in casting ingots that are to 
be forged, and for chill castings, as explained in the Chem- 
istry and hereafter. 

Non-metallic, 

But when the metal to be cast cools so quickly on contact 
with a metallic mold that it is apt to set up considerable 



2 XVIT. — FABRICATION OF ARTILLERY PROJECTILES. 

internal strain; when it is apt to form blow-holes; and par- 
ticularly, when its temperature is so high as to be destruc- 
tive to the mold, this must be made of sand. 

Because of its refractoriness, the sand used is generally 
silicious; and to increase its porosity to the gases, and its 
cohesiveness, that which is angular and of moderate size is 
preferred. Sand also yields slightly to the change in form 
of a casting while cooling. For example, a dumb-bell, cast 
in an iron mold would probably pull in two, from longitud- 
inal strain. 

Sand possessing all the properties to be desired for 
molding is seldom found in a natural state. Accordingly, 
artificial molding co77ipositions are made by mixing sand 
with various proportions of clay or flour to increase its co- 
hesiveness; or with some combustible material such as coal 
dust, horse manure or straw, to increase its porosity at a 
high temperature. 

The addition of water is necessary to give plasticity; but 
as this causes blcw-holes, and even dangerous explosions to 
occur, as little of it as possible is employed. In some cases 
it is removed h^j drying the mold; or, when great strength 
is required^ by baking it. 

Molding Compositions. 

The presence of water or of a combustible material in the 
molding composition exercises an important effect upon the 
casting. In both cases the gases resulting from contact 
with the molten metal act, as in the familiar example of 
water in the spheroidal state, to prevent close contact 
between the fluid metal and the particles of sand. The 
effect of this contact woujd be to make a rough, gritty 
surface, destructive to cutting tools. The combustible may 
be incorporated with the sand or applied upon the surface 
of the mold. 



XVn. — FABRICATION OF ARTILLERY PROJECTILES. 3 

^lolding compositions are divided into three classes: — 

1. Green Sand, which is wholly or nearly in its natural 
condition, and slightly damp. This is principally used for 
low grade castings, often molded in the floor of the foundry 
so as to avoid the use of flasks. 

2. Dry Sand, which is artificially dried after molding. 
This is used for cylindrical objects, cast vertically, as it per- 
mits a freer escape of gas than does the green sand. It is 
also used for castings of copper and brass on account of 
their greater conductivity, the object being to prevent their 
iooling as rapidly as in the moist green sand. For cohesion, 
a certam proportion of clay is mixed with the fresh sand ; 
and to compensate for the absence of water and the incor- 
porated carbon, sand which is of a fine grain is employed to 
give a smooth surface to the casting. 

3. Loam. This consists of a plastic mixture of clay 
and sand, to which straw, etc., are added for porosity. It 
is used for forming large volumes of revolution by the 
operation of sweep moldings to be described. Such objects 
are cast in pits, and hence the old sand resulting is called 
pit sand. 

Besides these there are ^v[\^^\o'^Q^^ parting sand 2^x\A facings. 
The former is lighter in color and of a finer grain than that 
employed in molding, and particularly free from moisture. 
Facings are generally composed of carbonaceous material, 
such as black wash, a mixture of finely ground coal and water, 
or of dry flour, soot, etc. ; though chalk is sometimes em- 
ployed on account of the CO^ it gives out when heated. 
Patterns. 

These are of two classes, according as they have a solid 
or a hollow form. The former may be called positive, and 
the latter negative patterns. As each kind of pattern is 
intended to produce its like in metal, the positive pattern is 



4 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 

used to form a negative mold, and the negative pattern, or 
core box^ to form a positive mold or core.^ 

To indicate in the mold the position which is to be occupied 
by the core, core prints are made on the surface of the pattern. 
These form cavities in the sand into which fit corresponding 
projections on the core. 

Positive patterns require to be made somewhat larger than 
the casting; the difference being determined by the shrinkage 
of the metal in cooling from the temperature of solidification 
to that of the atmosphere. 

To facilitate their withdrawal from the sand, patterns are 
given a smooth taper surface; the difference in diameter is 
called the draught. This requirement influences the number 
oi parts in which a pattern shall be made. 
Parting Plane. 

The parting plane is that in which the main sections or 
parts of the mold unite. The number of parts depends on 
the choice of the parting plane. Thus, for a rod of elliptical 
section, figure 7, if the parting plane contains either of the 
principal axes, AB, CD, there will be but two parts. But if 
the parting plane contains an oblique axis, as EF, either the 
mold or the pattern must be further subdivided. 

The parting plane is accordingly taken so as to include 
either the maximum or the minimum diameter of the pattern. 
Long cylindrical pieces are therefore parted on an axial 
plane, as this direction gives them abundant draught. 

The parting plane is the plane of reference for most of 
the operations of molding. 

Negative patterns part on an axial plane to facilitate the 
withdrawal of the core, which is often made truly cylindrical, 
or of a form not readily admitting ef its withdrawal in the 
direction of the axis. 



* This distinction is introduced only for purposes of instruction; th« 
©rdinary clfissifigation being simply, patterns and corgi. 



XVII. — FABRICATION OF ARTILLERY PROJECTILES. 



Material. 

The material of which a pattern is made depends upon 
the number of times which it may be employed, and some- 
what upon its size. If made of wood, it should be built up 
of pieces having the grain running in different directions so 
as to prevent its warping. 

In some cases where large castings are made by sweep 
moldings the expense of patterns may be spared, and the 
necessary concave and convex surfaces of revolution formed, 
by templets revolving about an axial spindle. The differ- 
ence of radii between the core and the mold so formed 
determines the thickness of the casting. 
Flask. 

The sand forming the mold is supported by an outer frame 
or box, called the flask. As many separate flasks are used 
as there 2iX& parts in the mold. 

For ordinary molding a two-part flask suffices; the part 
uppermost in casting being called the cope, and the lower 
part the drag. 

Lateral motion between the parts of the flask is prevented 
by dowels, and the cope is prevented from rising under the 
hydrostatic pressure of the melted metal by weights or 
clamps, or flanges bolted or keyed to the sides of the drag. 

The flask should conform to the general shape of the 
casting so as to avoid great differences in the rate of cool- 
ing and to facilitate the operations of molding. It often 
contains cross pieces to support the sand. 

For loam castings, the flask may consist of a pit, sunk 
beneath the surface of the foundry floor. 

Together with the flask is used^ as a temporary bottom, 
the folloiu board. This may have a plane surface next the 
flask, or may contain in relief one or more patterns so placed 
as to determine the proper position of the corresponding 
molds. 



6 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 

Molding Tools. 

These consist of shovels, watering pots and sieves for 
mixing the sand; rammers for packing it around the pattern: 
trowels of various forms for repairing imperfections, porous 
bags containing parting sand and facings, and venting wires 
with which to open an escape for the occluded gases. 

„ , II. MELTING. 

Metal. 

The properties of the metal employed depend on the size 
of the casting and the nature of the projectile. 

A decided advantage in tenacity follows the use of a large 
proportion of gun-steel scrap. 

The higher the grade of iron, the stronger it is; but the 
less fluid it is when melted, and the greater is the shrinkage 
and the difficulty of subsequently reducing it to finished 
size. The effects of shrinkage are relatively greatest in 
small molds. 

Consequently for field projectiles grey iron is used, and 
for those of larger size that which is more mottled or con- 
tains a larger proportion of white iron. For chilled shot a 
mixture is made of charcoal and anthracite pig irons, or of 
old shot and car wheels in about equal proportions. The 
components first named in each pair give toughness, and the 
latter the desired hardness to the casting. Car wheels are 
cast in chills surrounding the tread, while the centers are 
cast in sand. The chill gives hardness where abrasion is to 
be feared, and the sand causes the interior to cool more 
slowly, thus converting it into grey iron and giving it the 
softness and toughness required. The same principle is 
applied in the chill casting shown in figure 6. 

Furnaces. 

The cupola, or the reverberatory furnace is employed 
according to the quantity and quality of the projectiles;- to 
be cast. 



XVII. — FABRICATION OF ARTILLERY PROJECTILES. ? 

III. POURING. 

To diminish the shrinkage the iron is poured at the lowest 
temperature consistent with fluidity; and to make the shrink- 
age uniform, small ladles filled from the furnace are pre- 
ferred to the large ladles used for great castings. 

The melted metal is skimmed while pouring. 

FABRICATION OF PROJECTILES. 

To apply the preceding principles we will explain the 
manufacture of the 4.5 inch shot and shell of the Butler 
pattern, referring to figures 1 to 6. 
Patterns, 

The parting plane is taken at the junction of the body of 
the projectile and the tenon for the rotating ring; concen- 
tricity of these parts being secured by an axial dowel. 

The diameter of the cylindrical portion is enlarged rela- 
tively to the maximum diameter of the head; so that, during 
the reduction of the body to its finished size, the curvature 
of the head near the front bearing shall not be distorted. 

For the shot a teat provides a small surplus of metal near 
the point and ensures a full casting there. The teat is after- 
wards turned off to the curvature shown in the dotted lines. 

The shell pattern has a projecting spindle as a core print. 
This terminates at « in a conical surface, so that in spite of 
wear and unavoidable variations in manufacture it may be 
accurately centered in the cross piece,/, of the flask. Such 
conical bearings are frequently used in construction. 

As it is difficult for the sand to penetrate the small annular 
cavity above the main portion of the core, this is separately 
formed in the mold box ^ figure 4, before the spindle is seated 
in the core box. The mold box represented is of wood, 
constructed on the same plan as the core box. 

For a double-walled shell the core is covered with a cast 
iron corrugated sleeve of the form desired. The resistance 



8 XVn. — FABRICATION OF ARTILLERY PROJECTILES. 

which this offers to the contraction of the metal about it, 
explains why this ingenious form of projectile is not more 
largely employed. 

The patterns for the gate^ by which the melted metal is 
admitted to the mold, and the riser, by which the air and 
scoriae escape, are plain conical sticks, sometimes, as in figure 
6, made in two parts to facilitate their removal. 

Core Box. 

This is of iron, made in halves uniting on an axial plane. 
It is bored out when bolted together through the four holes 
shown, and brought into correct opposition by the four 
conical dowels near the holes. 

To form the core, an iron tube, called the spindle, per- 
forated with many holes and provided with a conical bear- 
ing as at a, (all figures,) is wrapped with tow and secured in 
the core box by a nut, n. Sand is then rammed around the 
spindle, the final form of the core being given by the cup, ^, 
so shaped as to strengthen the base of the shell. 

Flask. 

For large projectiles this is cylindrical; but for small ones 
it may be of rectangular cross section so as to contain several 
molds. For molding shell or cored shot, a cross piece, /, 
figures 5 and 6, containing a conical cavity, is so fixed in the 
flask that the parting plane of the pattern shall fall in the 
parting plane of the flask. For some projectiles, admitting 
of complete perforation, two cross pieces are provided. In 
such cases the conical bearings are not required. 

To give greater strength to the flask and to preserve the 
concentricity of the projectile the parting plane is one of 
right section. 

Position of the Pattern in the Flask. 

Shot are cast point down, so as to give density to the 
point- 



XVII. FABFICATION OF ARTILLERY PROJECTILES. 



Casting shell point down leads to porosity and weakness 
of the base which may cause them to fail in the gun. But 
when a front fuze is used, as in figure 5, if the shell were 
cast point up, the feeding of hot metal from the riser against 
the thinly protected spindle would soften it and cause it to 
bend. This objection does not apply when the fuze is in the 
bottom of the shell. 

On account of the difficulty of handling heavy chills^ 
chilled shot are always cast point down. To prevent the 
wear of the chill from the hot metal, which limits its life to 
about 50 casts, removable linings are employed. Following 
the general principle which requires a symmetrical arrange- 
ment of the parts of the mold, and to prevent its cracking 
from unequal expansion, the exterior of the chill should 
follow the profile of the mold. 

Gate and Eiser. 

For large projectiles, figure 6, the gate enters the mold 
preferably from below, so as to avoid splashing, and tangen- 
tially, to give a rotary motion to the ascending column of 
metal, and so sweep the scoriae away from its axis. 

The riser is intended: — 

1st. To allow free vent to the included air and gases. 
These are sometimes lighted to assist their dispersion. 

2nd. To allow the melted metal to be stirred during the 
solidification. This liberates the gases and scoriae; and, 
since fused metals are poor conductors, it facilitates simul- 
taneous solidification, and thus diminishes internal strain. 

3rd. To feed the hot metal into, and sometimes to make 
it flow through the mold. 

By careful stirring and feeding, shot as large as 12-inch 
have recently been cast solid. 

Small projectiles may be cast in groups with one gate for 



10 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 

several molds; but each mold should have an independent 
riser. 

Large spherical projectiles are sometimes cast in strings^ 
connected by necks which increase in diameter upward. 

OPERATION OF MOLDING. 

Secure the spindle of the shell pattern in its seat in the 
cross piece by the nut n. Invert the drag so that the shell 
shall rest upon the follow board on the parting plane. Place 
the main shot pattern upon the point of the follow board 
indicated by a dowel. Dust the follow board and the pat- 
terns with parting sand. Fill the mold, ramming it suffi- 
ciently to make it solid, but not so much so as to unduly 
diminish its porosity ; this requires much experience. 

Invert the drag, holding it between the follow board and 
another board. 

Remove the follow board; place the base patterns on the 
corresponding bodies and secure the cope by the dowels to 
the drag. Dust as before, and fill the mold; inserting the 
patterns for the gate and riser at the proper time. 

Place the follow board on the cope; lift off the cope and 
reverse it; remove the patterns which it contains: they may 
require to be slightly jarred, so as to loosen them in the 
sand. Do the same for the patterns in the drag. 

After repairing, drying, and facing the mold with black 
wash or its equivalent, place and secure the core which has 
been similarly treated. 

Replace the cope and secure it to the drag by such means 
as shown in figure 6. The mold is then ready for pouring. 

FINISHING. 

Preliminary Operations. 

As soon as the metal has become sufficiently solid, and 
while still hot, and therefore weak, the flask is opened 
and the excrescences left by the gate and riser broken 



XVII. — FABRICATION OF ARTILLERY PROJECTILES. 11 

off. To facilitate contraction about the core the spindle is 
withdrawn. This may be easily done, since the tow with 
which it was surrounded has been consumed. To retard 
the cooling of the casting it is then covered with the 
loose sand which formed the mold. When cool, the cavity 
is carefully cleaned from sand. 

The proper cylindrical form is given by the lathe, the 
most important of all machine tools. 
Description of the Lathe. 

A lathe is intended to form surfaces of revolution by 
causing an object to revolve on one of its axes while it 
is acted on by a cutting tool to which motion either along 
the axis of revolution, at right angles to it, or in both compo- 
nent directions may be given, either automatically or 
by hand. 

Figure 8 shows a lathe, in which A is the frame, the 
upper surface of which is formed in parallel rectilinear 
ways or guides. M, is the fixed head stock, in which 
revolves the cone pulley P. This may be made to carry 
with it the concentric live spuidlCy S, and the face-plate, 
F, or may revolve independently of these parts. The 
spindle is hollow and carries on its interior the conical 
center, C. Its exterior is threaded for the face-plate. 

T, is the movable tail stock; it contains the dead spindle, 
S, provided with a conical center like that in the live 
spindle. The tail stock may be clamped on the ways at 
any desired distance from Fj a close adjustment of S 
may be made by the screw Z>, which is clamped by the 
set screw E. 

The slide rest G, the invention of the great English 
mechanician. General Samuel Bentham, has been used for 
only about a century. To its invention is attributed the 
practical success of the steam engine; it having been pre- 
viously found impossible to produce truly cylindrical 



12 XVII. FABRICATION OF ARTILLERY PROJECTILES. 

surfaces of large diameter. The slide rest, carrying the 
cutting tool, derives its motion from the rotation of the 
live spindle by means of a change gear, H, which connects 
the outer end of the live spindle with the feed screw, J. 
The feed screw passes through a nut on the lower side 
of the slide rest, with which it may be thrown into and 
out of gear. 

Variations in Speed. 

The necessary cutting speed, or the velocity of the surface 
in contact with the tool, varies with the nature and diameter of 
the material to be turned. The angular velocity of the work 
may accordingly be varied by means of the steps on the 
cone pulley. A similar pulley above the lathe, with its 
axis reversed, receives the power from the main line of 
shafting by the driving belt, d, and transmits it to the lathe 
by means of the working belt, w. The upper pulley is 
mounted on an axis provided with a fast and a loose 
pulley, / and /, so that the lathe may be set in motion 
or stopped by varying the position of the driving belt. 
This arrangement, which is indispensable to all machine 
tools, is called a counter-shaft. See figure 9. 

Where great power, and therefore slow speed Is re- 
quired, the back gear, figure 10, is employed. This consists 
of two pinions, a and b, mounted on an axis, c, parallel 
to that of the spindle $, and so placed that when a engages 
with a toothed wheel, d, which is secured to the spindle, 
b, shall engage with one of corresponding size, g, upon 
the cone pulley. 

To use this, the cone pulley is detached from d, and 
revolves freely upon the spindle. The back gear may 
then be engaged with g and d. The ratio of the diameters 
of ^, b, a, d, indicates the resulting gain in power. 

By varying the change gear any desired ratio can be 
obtained between the angular velocity of the work and that 



Xvit. — ^Fabrication Of artillery projectiles. 13 

of the translation of the tool. In this way screws of any 
desired pitch may be cut. 
Support of Work. 

The work may be supported by the conical centers form- 
ing the adjacent ends of the live and dead spindles. For 
this purpose it is provided with corresponding depressions, 
which are called center niarks^ at the ends of the axis 
of revolution. As a rule these center marks are left in 
finished work, as they permit pieces containing them to be 
reworked or repaired. The work, in turning between 
centers, is caused to rotate by means of a dog^ figure 11; 
the tail of the dog fits in a radial notch in the face plate. 

In certain cases when turning between centers is impracti- 
cable, one end of the work is secured to the face plate 
by means of the chuck. This is provided with three radial 
set screws capable of simultaneous operation. See figure 12. 

In such cases, and to prevent the springing of long pieces 
in turning betv/een centers, an intermediate back rest^ By 
figure 8, is sometimes employed. 
Uses of the Lathe. 

It is evident that the lathe may be used for boring as 
well as for turning external surfaces, and that by the use 
of a hook-shaped tool, passed through the fuze hole, 
such cavities as that of the shell can be turned. 

Also, that plane surfaces can be formed by omitting the 
longitudinal translation of the tool, or that, preserving this 
motion and guiding the tool by means of a template, 
any desired surface of revolution may be exactly repro- 
duced. 

By replacing the center in the live spindle by a suitable 
tool, against which the work may be pressed by the back 
spindle, also without its center, the work may be drilled. 

If the tool be made after the manner of a very thick 
circular saw, the edge of which may be either cylindrical 



14 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 

or form almost any surface of revolution, the work may 
be moved along a plane director at right angles to the 
plane of rotation, so as to form a new surface composed 
of parallel rectilinear elements, and having its cross section 
correspond to the contour of the tool. This operation 
is called milling; it is of the greatest importance in the 
manufacture of fire arms, sewing machines and others in 
which the interchangeability of the parts is required. To 
the general use of milling machines may be largely attri- 
buted the eminence of certain American manufactures. 

The principal advantages of machines eniploying the 
principles of the lathe depend upon the continuity of 
the motion and the ease with which it may be varied. 

Final Operations. 

Projectiles of soft iron are finished externally on the 
lathe, or may be forced by an hydrostatic press through 
a circular steel die. The former method is preferred. The 
head is not touched, in order that the skin^ which is the 
hardest part, may remain intact. 

Chilled shot require special treatment by a grindstone 
or a peculiarly shaped prismatic tool, figure 13. This 
forms a scraping, instead of the paring edge generally 
employed; it is less apt to spring away from the work 
on meeting any portions which are excessively hard, and 
may be easily and accurately sharpened by a cylindrical 
grindstone. 

The natural silicious sandstone is frequently replaced 
by an artificial stone composed of emery concreted by a 
cement. 

FABRICATION OF STEEL PROJECTILES. 

Those are intended for piercing armor. Either cored 
shot or shell are employed. They may be either cast or 



3tvn. — Fabrication op ARtiLLERY projectiles. 15 

forged, The former are the cheaper; the latter, so far, the 

stronger. 

Steel Cast Projectiles. 

A rather silicious metal is preferred. In order to fix the 
carbon, both head and body are cast in a chill mold; this is 
surmounted by a sand mold containing the sinking head. 
After cutting off the sinking head, the projectile is hardened, 
the point being heated most. It is cooled by first dipping 
the point in water and then immersing the whole projectile 
in oil. In order to further soften the base so as to permit 
the screw thread in the fuze hole to be cut, the base is an- 
nealed while the point is kept in running water. To avoid 
this operation, the base of the projectile may contain a piece 
of wrought iron pipe, around which it has been cast, as in 
chilled shot. 
Forged Steel Projectiles. 

These are hammered into shape from bars of suitable size, 
turned inside and out, and hardened and tempered as above 
described. 

Steel shrapnel are now (1891) economically made by elec- 
tro-welding. Chapter XV, page 23. 

ROTATING BANDS. 

Copper is preferred on account of its softness and strength 
and its resistance to erosion by the gases. Its uniformity is 
increased by adding about 5 per cent of zinc. This forms 
an alloy known 2,% gilding metaiy used in the manufacture 
of cartridges, cheap jewelry and the bell buttons used in 
the Cadet uniform. 

The bands are applied in two general ways. 

I. In Casting. 

1. The band may be cast in place on the projectile. This is 
the simplest plan, but does not always make a good casting. 

2. An annular band, the cross section of which is as shown 



16 XVII, — FABRICATION OF ARTILLERY PROJECTILES. 

in figure 14, is placed in the bottom of the mold before the 
metal composing the body of the projectile is poured. To 
keep it from melting, it may be surrounded by a much thicker 
band of the same material, or by a hollow band through 
which runs a stream of water. 

II. After Casting. 

A seat for the band of the undercut section shown in 
figure 15, is turned in the body of the projectile and the band 
forced into this groove by hand or by machine. 
. 1. By hand. 

In this case the band may be either a straight rolled strip 
with bevelled ends, as seen in figure 16; or for large pro- 
jectiles it may be cast in the form of a semi-circular hoop. 
In both cases the placing of the band is done gradually by 
the hammer. 

2. By machine. 

The band complete is slipped over the projectile until 
opposite its seat; it is then set in by powerful presses acting 
radially. 

INSPECTION AND PROOF OF PROJECTILES. 
Comparison. 

It can hardly be too strongly insisted upon that the in- 
spection, not only of projectiles; but of powder and of arms 
of all kinds is only preparatory for and subordinate to, the 
proof. The inspection may detect the causes of failure in 
proof, and often applies to many more articles than can be 
profitably proved; but that it can not wholly replace it, is 
proverbially and actually true. 

INSPECTION, 

Object of the Inspection. 

The object of the inspection is to detect defects of work- 
manship and material which may affect the successful oper- 
ation of the projectiles. 



XVII. — FABRICATION OF ARTILLERY PROJECTILES. 17 

As it is impossible to make all projectiles of exact dimen- 
sions, certain variations are allowed in manufacture. For 
sake of economy, the greatest variation or tolerance^ con- 
sistent with safety and efficiency, should be allowed; both in 
workmanship, as shown by the gauges, and in the material. 
This remark is general. 
Instruments. 

Maximum and minimum ring gauges, see Chapter IV, page 
11; a hollow cylinder gauge, five calibers long; a profile 
gauge; a rolling table, and calipers for measuring the 
thickness of the metal at the sides and bottom of the cavity 
are the principal instruments required. Besides these there 
are various gauges to verify the dimensions of the fuze 
hole, and of the rotating device and its seat. Also various 
tools for exploring suspicious cavities or defects. 

An easy method of detecting small differences in the 
diameter of cylindrical holes consists in the use of a 
slightly conical bar of steel, the diameter of different 
sections of which is marked upon its length after the 
manner of a diagonal scale of equal parts. 

Except for the rolling table, the names of these instru- 
ments and their appearance as represented, figure 17, 
sufficiently indicate their employment. 

The rolling table is of iron with two parallel ribs at a 
distance apart slightly less than the length of the cylindrr- 
cal portion of the projectile. These ribs are brought truly 
level, so that a concentric projectile will assume a position 
of equilibrium of indifference. 
Process. 

The presence of fissures in hollow projectiles may be 
detected by exposing them to an internal jet of steam, or by 
observing whether after plunging them in water, notable 
differences in the rate of drying occur. 

When it is possible, the quality of the material is tested 



18 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 

by a specimen cut from the body of a projectile. For 
chilled shot this is not possible; so that a cast specimen 
may be tested and compared with those mixtures which 
have given good results. A certain proportion of such 
projectiles are also split so as to expose the chill. The 
homogeneity of such shot is also tested by striking them 
with a hammer at the junction of the body and head: a 
clear sound should be produced. In spite of the inspec- 
tion, such projectiles are liable to split spontaneously from 
internal strain. 

In order to stimulate the contractor to greater care, 
projectiles are inspected in lots^ the failure of a certain 
proportion of which for defects of material suffices to 
condemn the entire lot. This is then permanently marked 
so as to prevent its being again presented for inspection. 

This rule is applied also to defects in workmanship when 
the number of objects is too great to permit of the inspec- 
tion of every one, as in the ammunition for small arms. 

PROOF OF PROJECTILES. 

Careful inspection generally suffices for all but those in- 
tended for use against armor. But in all cases it is more 
conclusive to supplement this by a proof, as by firing for 
accuracy. 

Armor piercing projectiles are proved by firing about one 
per cent of a lot against wrought iron armor about one 
caliber thick ; the chilled iron striking normally and the steel 
at about 20 degrees to the normal. Upon the performance 
and endurance of the proof projectiles, fired with penetrating 
charges, depends the acceptance of the lot. 



XVIII. — MEANS OF COMMUNICATING FIRE. 



CHAPTER XVIII. 

MEANS OF COMMUNICATING FIRE. 

These may be divided into two classes, viz.; 

1. Those intended for igniting stationary charges in guns 
and mines. It includes various forms of matches and 
primers. 

2. Fuzes, which are intended to be used in moving objects, 
such as explosive projectiles, torpedoes, etc. 

CLASS I. 

MATCHES AND PRIMERS. 

According to the time elapsing between their own igni- 
tion and that of the charge, these may be considered as 
relatively slow or rapid. 

IGNITERS COMPARATIVELY SLOW. 

Slow-Match, 

This was formerly employed for igniting the port-fire, 
by which the loose gunpowder priming laid around the 
upper orifice of the vent was fired. It is now employed 
only for preserving fire. If made of hemp rope, combustion 
is retarded by saturating it with lead acetate, or the lye 
of wood ashes. If of cotton it is only necessary that 
the strands be well twisted. Slow match burns from 4 
to 5 inches per hour. 

Quick-Match is used to communicate fire, as in fire-works 
and in experimental work of a dangerous character. It 
is made of candle wick, steeped in a mixture of mealed 



8 XVm. — MEANS OF COMMUNICATING FIRE. 

powder and gummed spirits, wound on a reel, dredged 
with mealed powder and left to dry. ^t burns at the rate 
of about 3 inches per second. 
Varieties of duick-Match. 

The rate of burning may be much increased by enclos- 
ing the quick-match in a paper tube; see Chapter VIII. 

If, instead of paper, the envelope be made more pliable 
and strong, as by a spiral wrapping of cloth around a 
central core of fine powder, the ordinary blastings or Bick- 
ford fuze results. This inflames at a less rapid rate than 
the kind just named. 

A tube of lead or one of its alloys may replace the 
weaker envelopes above described and instead of simply 
fitting it closely, the tube, enclosing the core, may be 
drawn as one mass after the manner of wire. 

If gun-cotton be used for the core, a most convenient 
and rapid form of detonator results. 

IGNITERS COMPARATIVELY RAPID. 

Caps and Detonators. 

These consist of cups or tubes made by means of a 
double punch, figure 1, the inner member of which, /, 
passes through a conical hole, h, of somewhat larger diam- 
eter in a stationary piece, d^ called a die. The outer 
punch,/', which is concentric with the inner and fits closely 
to it, as it descends into a shallow cylindrical depression 
at the mouth of the die, shears from a thin copper ribbon a 
disc which it holds by the edges while the inner punch forms 
it into a cup. The elasticity of the cup causes its open end to 
expand as soon as it has passed through the die : this strips 
it from the punch as the latter rises for another stroke. The 
cup is elongated into a tube by the successive operation of a 
series of single punches and dies of gradually decreasing di- 
ameter, See plates Chapter XXVII, This operation, which 



XVIIl.— MEANS OF COMMUNICATING FIRE. 3 

resembles closely that of rollings in chapter XV, is of great 
utility in the arts. For military purposes it is principally 
used in the manufacture of metallic cartridges. 

For percussion caps for small arms, the tube receives 
a charge of moist fulminating composition. This is pre- 
vented from falling out, when dry, by a disc of tin foil, 
held in by varnish. 

The construction of the detonator has already been 
described in chapter XIV. 
Cannon Primers. 

These are of two classes, according as they are fired 
by friction or electricity. 
I. Friction Primers. 

The friction primer presents the following advantages 
over the method of firing cannon described, page 1. It 
is portable, certain and rapid; it affords the means of firing 
pieces at a distance, and does not attract the attention of 
the enemy's marksmen at night. 

According to the direction of the vent, friction primers 
are divided into two classes. 

I. Radial Vent. 

The primer used in the military service of the United 
States consists of two copper tubes, soldered at right angles 
to each other, figure 2. 

The short tube contains a charge of friction composition, 
(Sbg S3 and K CIO3) inserted moist and surrounding the 
roughened end of a wire, the outer extremity of which 
forms a loop for the lanyard. The long tube is filled with 
fine powder, retained by a wad of wax. The nib of the 
wire is folded over the end of the short tube, so as to 
prevent its accidental displacement and the firing of the 
composition in consequence. 

For large guns, the column of fine powder may surmount 



4 3^\ltt.--MEAMS OJ* CoMMttNlCATmc MVlU. 

a pellet of compressed powder which will be shot, burning, 
into the cartridge. 

In some services the cross tube is omitted and the wire, 
inserted axially, is withdrawn by a motion which causes it to 
bend continuously around the edge of the vent. See 
figure 3. 

2. Axial Vent, 

As the discharge serves to expel the empty tube with 
great velocity, unless it be thrown upward it may injure 
the bystanders. On this account, and also to prevent the 
erosion of the vent by the escaping gas, an ohtwating prbner 
is screwed into a proper seat concentric with the vent. 
Figure 4 represents an obturating axial friction primer. 
When the wire is withdrawn, the conical portion, c, finds 
a corresponding seat at the end of the cavity surrounding 
the wire. This prevents the escape of gas through the hole, 
while the escape around the primer is prevented by the 
radial expansion of the thin edge in which the portion 
nearest to the charge is formed. 

The stop, ^, prevents the primer from being screwed in 
too far, and the enlargement, ^, serves a similar purpose for 
the wire. 
II. Electric Primers. 

These are used for firing charges at a considerable 
distance, as in certain cases in modern warfare when the 
gun is so protected that the object is invisible from its 
neighborhood; so that the pointing and firing are controlled 
by a distant observer. By this means also, the simultaneous 
discharge of several cannon at a common object may 
greatly increase their effect. A similar advantage follows 
in mines. 

The primers are of two general classes: 

I. High tension, in which ignition results from the pass- 
age of the electric spark between the disconnected ends 



XVIII. — MEANS OF COMMUNICATING FIRE. 5 

of two insulated conductors. For this class the conductors 
require careful insulation and to be separated from adjacent 
circuits, so as to prevent the primers in one circuit from 
being accidentally exploded by currents induced from the 
other circuits. 

2. Low tension^ in which ignition results from the heating 
of a short wire of high resistance which connects the ends 
of the conductors. Owing to the ease with which the con- 
dition of the circuit can be tested before firing, and the 
comparatively low electro-motive force of the currents 
employed, this is the only class of electric primer used 
in artillery. 

Figure 5 represents a common electric primer, and figure 
6 an obturating electric primer. The platinum wire is 
coiled to facilitate its handling in manufacture. It is sur- 
rounded by a wisp of gun-cotton. 

The obturating plug,/, of hard rubber seals the channel 
by being pressed against the sharp ring in rear. In other 
essentials these primers resemble figures 2 and 4:. 

MEANS OF IGNITING PRIMERS. 

If quick match be used it sufiices to unite the lines so 
that the distances B C, B C, B C\ etc., in figure 7; or 
BC^ B D C, figure 8, be equal. If the detonating tubes, 
page 2 be used, these precautions are unnecessary. 

For electric primers the voltaic battery is generally 
employed, although for experimental purposes a small 
portable dynamo or frictional apparatus is very convenient. 

When it is desired to be able to fire without delay, a 
battery is preferred, which, like the Leclanche, can be kept 
for a long time in open circuit without sensible change and 
which only needs the circuit to be closed to produce the 
effect desired. 

In using the electric current in direct or continuous circuit 



6 XVIII — MEANS OF COMMUNICATING FIRE. 

as in figure 9, the number of cells of the battery required 
increases with the number of primers, /,/',/", and it may 
happen that the most sensitive of the primers, exploding 
first, will cause the remainder to fail. 

For the second reason a derived, or parallel circuit, as 
in figure 10, is preferred. The successive explosion of the 
more sensitive primers increases the current which passes 
through each of the remaining primers, since their number 
is diminished. 

In order to employ a weaker battery, the arrangement 
shown in figures 11 and 12, serves, by sweeping the key, ky 
over the ends of the terminals, to produce a practically 
simultaneous discharge. 

CLASS II. 

FUZES. 

Fuzes are employed to explode the bursting charge of a 
projectile at any desired point of its trajectory. They may 
be classified, according to their mode of operation, as timey 
impact and combination fuzes. 

I. TIME FUZES. 

A time fuze contains a column of com.position, which, 
having been ignited at the discharge of the piece, after having 
burned for a definite time, ignites the bursting charge. 

Requisites. 

Such fuzes are principally employed to burst projectiles 
while in the air; they therefore require that the relation be 
known between the distance to the point of explosion and 
the time of flight, and that the column be taken of such a 
length that it will burn in the time so determined. 

The first of these requisites involves the estimation of the 
distance by various systems of range finding, and the deter- 



XVIII. — MEANS OF COMMUNICATING FIRE. 7 

mination from Ballistics of the required angle of projection 
and the time of flight to the point desired. The second 
requirement demands that the rate of burning be known, 
and, since the time of burning is varied by varying the 
length of the column, that the rate be uniform throughout 
its length. Finally, that the column be taken of the exact 
length required by the rate, and that it both receive and 
impart fire with certainty. 

The principal points to be considered in the development 
of time fuzes are, that as we increase the muzzle velocity 
and sectional density of our projectiles, the longer will be 
the maximum time of burning required for the fuze. As 
the remaining velocity increases, the greater will be the error 
in distance due to a given error in time; and the greater the 
range, the more difficult will it be to detect the error in 
distance. Therefore improvements in cannon require corre- 
sponding improvements in the uniformity of rate and in the 
exactness of the length of the burning column. The greater 
the rate of burning, the larger the scale and therefore the 
smaller the effect of a given error in cutting. 

The rate is so much affected by the conditions relating to 
the resistance of the air during flight, that, while uniformity 
of rate may be indicated by the tests of manufacture, the 
lengths of column for given ranges should be determined by 
actual trial in the gun. On this account, and to avoid com- 
putation in the field, when the initial velocity and sectional 
density are fixed, the scale is preferably one of ranges, in- 
stead of units of time. 

The great efficiency of projectiles properly exploded in 
air, as explained in Chapter XVI, and the experience gained 
with smooth-bore cannon, in which this was the only form 
of fuze that could be successfully used, account for the pains 
that have been taken to meet these requirements ever since 
the early days when the fuze was lighted before loading. 



8 XVIII. — MEANS OF COMMUNICATING FIRE. 

Kate of Burning. 

This will depend upon the conditions named Chapter 
VIII, page 3. 

The rate was formerly varied by varying the composition, 
but as any departure from the usual proportions is found 
to diminish the uniformity of the rate, to increase the 
difjficulty of preservation, and to increase the amount 
of residue, it is now thought best to vary the rate only 
by varying the amount of incorporation and the density 
of the composition. 

When the total time of burning is very great, as in some 
of the large mortar projectiles, which may be 40 seconds 
in the air, a return to the variable composition appears 
necessary. 

Former Practice. 

For spherical projectiles the column was cylindrical and 
was ordinarily contained in a conical case of paper, wood or 
metal. This was filled with small successive quantities of 
mealed gunpowder which were compacted by a drift upon 
which a given number of blows were struck by a mallet. By a 
repetition of the process the case was gradually filled. 

The exterior of the case was divided into equal propor- 
tionate parts by which to regulate the time of burning, 
either by cutting off the case; or, since the entire column 
might then be dislodged backward into the cavity of the 
shell by the shock of discharge, by boring into it with a 
gimlet. 

The fuze was ignited by a priming of mealed powder 
placed so as to catch fire from the flame passing through 
the windage of muzzle-loading guns, both smooth-bore and 
rifled. 

The method of filling caused variation in fuzes of the same 
kind, and even between different sections of the same fuze. 



\ XVIII. — MEANS OF COMMUNICATING FIRE. 9 

1 ' ~ 

\ 

Exv.mples of Fuzes for Muzzle-loading Projectiles, 

Figures 13 and 14 illustrate two varieties of time fuze, in 
one of wUch the composition was fixed in the case and in 
the other v^as movable. 

The Mortar fuze case or plug was made of a close grained 
wood, like beech, bored out nearly to the bottom. The 
top of the cavity was enlarged to receive the priming of 
mealed powder and alcohol. This was covered by a cap 
of waterproof paper on which was marked the rate of burn- 
ing. For economy of manufacture the exterior of all 
mortar fuze plugs was marked in inches and tenths, instead 
of with reference to the rate of burning of their contents. 

The Sea Coast fuze consisted of a brass plug containing 
a separate paper case, filled with a composition of variable 
proportions and bearing on its exterior a scale of times. 
The mouth of the plug was closed by a water-cap, per- 
forated by a zig-zag channel. This was also filled with 
mealed powder for the ignition of the fuze; but was so 
constructed as to prevent the composition from being 
extinguished in the ricochet fire over water, largely em- 
ployed in former times. 

These fuzes answered well for the comparatively low 
remaining velocities and short ranges usual when spherical 
projectiles were employed; but they required valuable time 
for their adjustment and were imperfectly protected from 
the effects of excessive heat or of moisture while in store. 

The Bormann fuze, figure 15, was invented to overcome 
these and other objections. The case being of pewter is un- 
altered in size by meteorological changes, and it contains 
the composition in a channel, which, though air tight, can 
be readily cut by a proper tool. The circular form of the 
column and its diminished section allow the size of the case 
to be reduced, and the composition to be compressed in the 
direction of its shortest dimension. The mean density of 



10 XV^I. — MEANS OF COMMUNICATING FIRE. 



the succe^ssive layers estimated in the direction of the com- 
bustion is thereby made uniform. The case is screwed into 
the fuze hole by a screw driver, the prongs of whxh engage 
into the recesses a, a. 

The graduated arc lies over the circular column of 
mealed powder which, after compression, is covered by the 
tightly fitting wedge shaped ring, b. The only outlet to 
the channel is under the zero of graduation; this outlet, r, 
and the magazine^ m, are filled with fine powder which is 
retained by a disc of tin, e. 

To enable the fy^e to resist the shock of discharge, to 
which its softness, density and form render it especially 
weak; and also to increase the effect of a small bursting 
charge, the lower portion of the fuze hole is closed by a 
perforated disc,/. 

The objections to the Bormann fuze are the short time 
of its burning; the uncertainty of its ignition unless it 
be carefully primed, and that, once set for firing, it is use- 
less for any greater time of flight. 
Present Time Fuse. 

The use of breech-loading cannon necessarily prevents 
the ignition of the fuze through the windage so that a special 
device called an inertia igniter is employed for that pur- 
pose. Its operation is illustrated in figures 16 and 24. 

In figure 16 the inertia igniter consists of a mass of lead 
containing a pellet of fulminate and supported a short dis- 
tance above the sharp point, /, by some device which, while 
stable against ordinary shocks, will be surely moved by that 
of discharge. This device may be either a spiral spring or a 
transverse pin of brittle material. 

The flame from the fulminate escapes through the holes^ 
h, into the annular cavity, r, and, by a hole on the inner 
surface of the ring, r, ignites the circular column of com- 
position which the rmg contains. 



XVIII. — MEANS OF COMMUNICATING FIRE. 11 

The exterior surface of the ring is graduated, as in 
seconds, and the body of the fuze contains a mark, placed 
opposite to the entrance to the magazine, w, so that by- 
setting the ring before firing with any division of its scale 
opposite to the mark, the length of the burning column is 
fixed. The cap, k, is used to c^amp the ring in place. 

To prevent the opposing rush of the gases from the two 
sections of the burning column, it is ignited at one of its 
ends; this permits a free escape of the gases to the outer 
air through a hole previously temporarily sealed against 
moisture. 

Figure 17 shows the course taken by the escaping gases 
when the burning surface moves, as in the Bormann fuze, 
in two directions from the hole, ^, to the magazine, m^ 
Figure 18 shows the improved method. 

For long ranges, since the form of the projectile permits 
its length to be indefinitely increased, the fuze may contain 
two or more rings arranged in tiers. 

II. IMPACT FUZES. 

Concussion Fuzes. 

Until the introduction of rifled projectiles many unsuc- 
cessful attempts were made to combine the time fuze with 
some device which would be safe when the gun was fired; 
and yet, if the time fuze failed to act at the proper point, 
would explode the bursting charge on impact. 

Owing to the uncertainty of the direction of the impact 
such fuzes are called concussion fuzes to distinguish them 
from the percussion fuzes now generally employed. 
Percussion Fuzes. 

Although as stated, Chapter XVI, page 21, the shock of 
impact may in certain cases suffice to explode the bursting 
charge, it is much more certain to employ a special appa- 
ratus for this purpose. 



12 XVIII. — MEANS OF COMMUNICATING FIRE. 



Although more complicated in structure than time fuzes, 
those of the percussion class act with more certainty since 
the conditions to be fulfilled are more easy of accomplish- 
ment. They are not as subject to deterioration in store, 
and, since they are usually entirely automatic, they require 
no preparation before firing. By the volume of smoke 
resulting from the explosion of shells containing percussion 
fuzes, the gunner is afforded one of the readiest means 
of correcting his aim. 

Percussion fuzes are divided, according to their position 
on the projectile, into fronts or base fuzes. The former 
possess the advantage that on impact, the bursting charge is 
thrown towards the fuze ; the latter class is required for pro- 
jectiles to be used against armor. 
Requisites. 

A good percussion fuze requires — 

1. A case to hold and guide the movable parts, and to 
protect them from being clogged by the dust arising from 
the bursting charge in transportation, and by the earth 
against which they may strike. 

2. A plunger, by the motion of which, on impact, the 
charge is fired. 

3. A fulminating composition, ignited by the plunger. 

4. The priming, a charge of fine powder ignited by the 
fulminate and serving to increase the certainty of the 
ignition of the bursting charge. 

5. A safety device, by which the accidental dislodgement 
of the plunger is prevented; but which will certainly free 
the plunger when the piece is fired. 

6. A device to prevent the plunger from moving forward 
in its cavity during flight. This tendency results from the 
greater retardation of the projectile than of the enclosed 
plunger by the resistance of the atmosphere. The effect 
of this relative motion may be to cause a premature explo- 



XVllt.— MeA^§ of COMMtJi^lCAftNG FIRE. ' 13 

sion if the fulminate is sensitive; or else on impact to 
deprive the plunger of sufficient motion to cause the explo- 
sion of a fulminate, the sensitiveness of which, for the reason 
above given, has been diminished. 

The most difficult of these requisites to provide is the 
safety device. In the early percussion fuzes the plunger 
was a single mass sustained by a transverse pin or by lugs 
cast upon it. The pin was made strong enough to stand the 
shocks of transportation; but was shorn off by the shock of 
discharge. The mass to be given to the plunger was determ- 
ined by confficting considerations. If made so light as not 
to be liable to shear its support by accident, it might fail 
to explode the fulminate when impact occurred at a low 
velocity. The advantage of a proper distribution of func- 
tions among the parts of the apparatus appears from the 
following discussion: 
Type of Improved Percussion Fuze. 

Let Fhe the initial velocity of the projectile and v, and 
z;', its velocities on impact, and after impact, as in the 
ricochet. 

Let m, be the mass of the plunger and p/ that of the 
safety device: this we will suppose to be a hollow cylinder 
as in figure 19, surrounding the upper part of the plunger, 
but kept from moving backward upon it by a suitable pro- 
jection, as that upon the flat spring, s\ In the type selected 
the section of the plunger is square and fits the hole in the 
safety device. 

When the piece is fired, m' moves relatively to the rear 

with an energy which, on account of the large value 

2i 
of Vj is capable of overcoming a resistance great enough to 
be absolutely safe against all accidents of transportation. 
In so doing it becomes solidly united to m, so that when 
impact occurs, although v—v' may be much less than F", 



14 Xvm.— MEANS OF COMMUNICATING FIRE. 



the energy — - — {v—v'Y may easily overcome the resist- 

ance of the spiral springs, and so ignite the fulminate,/, 
and the priming,/. 

If, during the flight of the projectile m' does not remain 
relatively at rest its conical form tends to make it roll 
rather towards the base of the cavity than away from it. It 
is also urged in this direction by the spring s. 

This fuze, which is of French origin, represents one of 
the best existing types. It requires a value of V not less 
than about 1000/. ^., and therefore is somewhat more com- 
plicated in construction when projectiles containing it are 
fired with low velocities. 

Percussion Fuzes used in the United States. 

Hotchkiss Front Percussion Fuze. Figure 20. 

A, is the case, closed in front by the screw-cap B, and 
with a conical hole in rear closed by a lead safety plug C. 
Dy represents the plunger, composed of lead cast into a 
brass jacket to prevent its dilatation by shock, 

A continuous brass wire, E, the upper portion of which 
is bent in a semi-circle concentric with the plunger, is cast 
into the lead and supports the plunger in the case. The 
lower ends of the wire are securely held by the friction 
of the safety plug against the sides of its cavity. At 7% is 
the fulminate, and at F, the priming. 

When the piece is fired, C, is dislodged backward into 
the interior of the cavity either by its own inertia or by the 
blow received from F). The wires spread outward and 
prevent the plunger from moving forward until the pro- 
jectile strikes a sufficiently resisting object. 

Hotchkiss Base Percussion Fuze. Figure 21. 

The case. A, carries the fulminate, F, in a large percus- 
sion cap contained in the perforated screw-box^ which is 



XVIII.— MEANS OF COMMUNICATING FIRE. 15 

formed in two sections, G and JI. The base of the case is 
provided with a projecting flange, /, brought to a thin edge 
which, when the fuze is screwed home, acts as a gas check. 
The plunger Z>, is made as in figure 20, but contains a 
central firing-pin, Z, roughened so that it will hold well 
in the lead. 

The rear end of the firing-pin projects beyond the bottom 
of the plunger, while its front end is sunk a little below the 
surface so that when this compound part {D and L) is in 
place, it is prevented from moving by the screw-box. 

When the gun is fired the plunger slides back on the 
firing-pin so that the point projects above the plunger. 
The lead being soft, and being prevented from expanding 
by the jacket, it takes a fresh hold on the pin and supports 
it when it is thrown forward on impact. 

This fuze has certain structural defects which render 
its operation less certain than that of the front fuze. For 
its special purpose it is probably one of the best known. 
Krupp Fuze. 

Figure 22 shows a Krupp fuze in a double walled shell. 
Safety in loading results from the transverse pin, /, which, 
with the screw-box containing the fulminate, is inserted just 
before loading. The rotation of the projectile expels the 
pin, leaving the longitudinal pin,/, free to be driven inward 
on impact so as to prevent the entrance of earth into the 
cavity of the fuze. The nomenclature of figure 22 is the 
same as that of figures 20 and 21. It is said that this 
pattern is to be replaced by one containing a safety device 
which is intended to be unscrewed by the rotation of the 
projectile. 

III. COMBINATION FUZES. 

These combine the principles of the time and impact fuzes 
50 as; — 



16 XVIII. — MEANS OF COMMUNICATING FIRE. 

1. To increase the probability of explosion; since, if the 
probability of a failure in each of the two cases be, say, 0.01; 
that of the combination will be 0.0001. 

2. To permit the character of the firing to be rapidly 
varied, 

3. To increase the certainty of explosion when the pro- 
jectile is fired with a low velocity. 

Figure 23 illustrates one of the most recent combination 
fuzes used in the French service. 

^ is a leaden fuze tube made as d^escribed page 2. It is 
wrapped spirally about, and secured to the hollow cone, C; 
this is held in place by the clamp screw, D. The lower end 
of the fuze tube communicates through the priming, /*, with 
the cavity in which lies the percussion fuze described page 13. 

The inertia igniter consists of a loose, pointed piston, ZT, 
which, until the instant of discharge, is separated from the 
fulminate, F^ by the spiral springs .S". 

K^ is a conical cap pierced with a series of numbered holes 
corresponding to the times of burning and provided with a 
vernier for interpolating a puncture between any two holes. 
The puncture, owing to the softness of the metal of which (7, 
is composed, is made entirely through both its walls. 

When the piece is discharged, the washer of compressed 
powder, W^ is ignited by ZT, and through the puncture the 
fire extends to the composition in E. At the same time the 
percussion fuze acts as before described. 

But for the union of the two fuzes in the same case, which 
the construction of the projectile and the operation of front 
percussion fuzes requires, this fuze illustrates the principle 
referred to Chapter XVI, page 34. The simplicity of con- 
struction, which was formerly considered of prime impor- 
tance, has been entirely subordinated to efficiency of oper- 
ation, notwithstanding the greatly increased cost which this 
involves. 



XVIII. — MEANS OF COMMUNICATING FIRE. 17 

The Flagler Combina^tion Fuze. Figure 24. 

This fuze, devised by Colonel Flagler of the Ordnance 
Department, is now, 1889, undergoing trial. It combines 
many of the principles just discussed and adds two new 
features to provide for the requirements numbered 5 and 
6, page 12. 

The first feature consi^s of a copper wire, d^ screwed from 
the rear into the open end of the screw-cap^ A. The lower end 
of this wire is bent at right angles so as to support firmly 
the leaden time plunger, D. Just below the screw thread 
by which it is suspended the diameter of the wire is reduced 
to any desired extent. 

The wire is broken at the neck so formed by the stress 
due to the acceleration of the projectile, both in translation 
and in rotation. The latter stress, occurring only when the 
piece is fired increases the certainty of ignition without 
diminishing the safety of the apparatus against accidental 
shock. 

On firing, the mass, Z>, is thrown against the fixed firing 
pin, F^ and the fulminate ^^, is ignited. The flame from 
the fulminate escapes through the radial holes and the an- 
nular channel, ^, b^ to the end of the column of composition 
projecting into the radial groove, Z, formed on the lower 
side of the ring, or carcass C. The gas first formed blows 
off the vent cover, ^, and allows the remaining gases to 
escape freely. 

When the column has burned to the point, b\ corre- 
sponding to which there is a fixed mark on that portion 
of the body next to the graduation on the ring, the priming 
K^ is ignited and the flame from it passes down the fluted 
surfaces of the members, G^ H^ 7, of the percussion fuze 
into the bursting charge. 

The advantage claimed for this safety device over those 
in which ears projecting from the mass Z>, are shorn off by 



IS XVIII. — MEANS OF COMMUNICATING FIRE. 

the shock of discharge, refers to the uniformity of copper 
wire and to 'the absence of the loose pieces, which, after 
shearing has occurred, may impede the action of the 
plunger. 

The percussion fuze resembles the Hotchkiss base fuze, 
with the following advantages: — 

1. The priming K, which serves for both fuzes of the 
combination, makes the volume of the flame on impact 
much greater than when fulminate only is employed. 

2. In order to fulfil requirement 6, page 12, a disc of thin 
zinc separates the point of the firing pin, h, from the fulmi- 
nate above it. This presents a positive and uniform 
resistance to premature explosion; and, since a pressure of 
6 pounds is required to pierce it, the fulminate may be 
made as sensitive as may be desired. 

3. On impact the powder is thrown toward the fuze. 
The fuze works well in practice. The percussion fuze 

was found to operate when the projectile was fired through 
a 2-inch board, though it failed in penetrating a board one 
inch thick. It is thought that it will explode on striking 
animate objects or sandy or marshy ground. 

GENERAL REMARKS. 

Owing to their greater permanency of form in store, and 
their diminished volume, metallic cases are preferred to the 
wooden ones formerly employed. 

In order to cheapen the manufacture, which at best is 
very expensive, the parts are, whenever possible, made of 
pewter, cast in metallic molds into finished forms. When 
strength and infusibility are required, brass or bronze are 
used, cast as described in Chapter XVII. 

To prevent unscrewing during flight, the screw thread of 
base fuzes should turn in a direction contrary to that of 
the rifling. 



3tvni. — MEANS O^ COMMttNlCATiNG f'lRE. 19 



It takes an appreciable time after impact for tLe explo- 
sion to occur; so that even when the fulminate was pur- 
posely ignited by the shock of discharge, the shell did not 
burst until it had gone several yards beyond the muzzle of 
the gun. This is of importance in understanding the effect 
of shrapnel fire with percussion fuzes, and serves to show 
that explosions within the gun generally result from defects 
in the construction of the projectile. 

To prevent premature explosion from the plunger's 
being thrown violently forward by the elasticity of the 
bottom of the shell, on discharge, a perforated cardboard 
washer is often required. 

A percussion shell, unexploded in experimental firing 
should never be tampered with: if possible, it should be 
exploded on the spot by a dynamite cartridge. 



X15t. — GDN CoKstktrcTioN. 



CHAPTER XIX. 

GUN CONSTRUCTION. 

Nomenclature of Stresses. 

The total pressure of the powder gases in a gun may be 
analyzed as follows with reference to the direction of the 
resulting strains. 

1. A radial stress, known by the special name of 
"pressure" (/). 

2. A tangential stress, or hoop tension (/) which tends 
to split the piece open longitudinally, being similar in its 
action to the force which bursts the hoops of a barrel. 

3. A longitudinal stress ((/) which tends to pull the piece 
apart in the direction of its length. 

4. Besides these, which are the principal stresses now 
considered, was formerly treated the transverse stress which 
tends to bend outward the staves of which the tube may be 
supposed to consist. 

Its effects are so closely associated with the strains above 
named that it is no longer discussed. 

Of the principal stresses named the most important is the 
tangential, since it is that from which failure most readily 
occurs. 

BARLOW'S LAW. 
Limitations. 

This law, which was until recently applied to the con- 
struction of homogeneous cannon, if confined to stresses 
beneath the elastic limit, (Chap. XV, p. 11,) under which 



XIX. — GUN CONSTRtJCTIOl^. 



limit the stresses are taken to be proportional to the strains, 
gives results which agree fairly well with those obtained by 
the more exact methods now generally employed. 

But, when applied to built up guns composed of concentric 
cylinders assembled by shrinkages as described in Chap. XV, 
it is no longer generally used because it does not analyze 
the resultant strain into the component strains occuring in 
three coordinate directions. For example, if we compress a 
cube in the direction of the axis of Z, there will be deyeloped 
along the axes of X and Y component strains correspond- 
ing to tensile stresses acting in each of these directions and 
conversely. 

On account of the relative simplicity of Barlow's law it 
will be employed to illustrate the general principles of gun 
construction. A more extended discussion of the theory now 
accepted will be found in the appendix of this chapter. 



DEDUCTION OF BARLOW's LAW. 

Hypotheses. 

Suppose — {a) the piece to be a hollow cylinder of homo- 
geneous metal, and — {h) that the effect of a central force be 
transmitted outward in such a manner as to make constant 
the area of cross-section by a plane perpendicular to the 
axis. 

{a) The homogeneity of the metal Is required, so that a 
constant relation may exist between stress and strain ; or that 
the coefficient of elasticity, known herein as E^ may remain 
constant. 

{h) The constancy of area or cross-section resembles 
the assumption that the various stresses, from the effects of 
which the physical properties of the metal are determined 
in the testing machine, continue to be applied to the original 



XIX. — GUN CONSTRUCTION. 



area of cross-section ; although it is evident that, if the volume 
of the metal be constant, its area of cross-section must 
diminish or increase when exposed to tensile or compressive 
stress respectively.* 

Wertheim's experiments show that the developed strains 
are each — ^ of the principal strain. 
Preliminary Statement. 

Suppose that figure 1 represents a section of a homogen- 
eous gun after firing: the radii R and >^' having been ex- 
tended to r and J^" so as to maintain the sectional area 
constant. 

Then, the area whose limiting radii are r and E' being 
common to both states of the section, we have 
TT (r^ _ i?^) rr TT {R" » — R' '), or 
(r J^R){r—R) = {R" + R') {R" — R'), 

But since R" and R' are each greater than either R or r 
R" + R'y r-\-R 

,'.r—RyR"^R', or 

2 TT{r—R) __ r—R R" — R' 
27rie ~". i? -^ R' 

The two members of this inequality measure the strains 
on the interior and exterior surfaces respectively, so that it 
appears that the surface of the bore might be strained be- 
yond its elastic limit before that of the outside layers was 
reached. 

The resulting set, if slight, might destroy the accuracy of 
the piece from the dilatation of the bore; and, if consider- 
able, it might lead to the formation of fissures which would 



*Throughout the following discussion we will consider that we are 
dealing with a cylinder of but one unit of length, since, as the length of 
the cylinder varies, both the pressure tending to burst the cylinder and 
the resistance which it opposes will vary in the same ratio. 



XIX. — GUN CONSTRUCTION. 



facilitate the final rupture in detail of the successive cylin- 
drical layers of which the gun may be supposed to consist* 
The considerations explain the statement in Chapter V, 
as to strength vs. weight. 

Analysis. 

To determine the law by which the tangential stresses 
are distributed throughout the section of a gun: — 

Let J^ and Z be the radius and the circumference of the 
bore. Let /<, be the radial pressure per unit of area and 
T the tangential stress on the surface of the bore. Let r, Zy 
p and / represent the same quantities on any exterior 
cylindrical surface, the area of cross-section between which 
and Z is A. Then by assumption, {fi) above 

Tt {f— B}) ::^ A, and .*. rdr = RdR. 

Multiplying the first member of the last equation by -, 

and the second member by -^ we have r^ — = i?^ -^ . 

'' R r R 

I But, since the ratio between the circumference and the 

radius is constant, and since beneath the elastic limit the 

stresses are proportional to the strains 

, dr dz t . dR T 

i - = V = ^ ""^ ■:ff = ■:£ 

Therefore, we have 

tf^ TR^ , TR^ 

_ = — or/=-^ (1) 

Or, since under given conditions of /o? ^ and i?, TR^ 
will be constant, the tangential stress {or strain) on each sue- 



* This last statement, though generally true, is subject to modification 
depending on the ductility of the material and the development of special 
elasticity. See post. 



XIX. — GUN CONSTRUCTION. 



cessive concentric elementary cylinder varies inversely with the 
square of its radius. ' This is Barlow's law. 

This condition may be represented by figure 2, in which 
the ordinates of the curve T T' represent the tangential 
stresses on the corresponding circumferences. 

In this figure and in those succeeding it, positive hoop 
tensions are represented by ordinates laid off above the line 
representing the trace of the axial plane of least resistance, 
and negative hoop tensions (compressions) are laid off below 
this line. See figures 5 and 6. 

RESISTANCE OF THE CYLINDER., 

Bursting Effort. 

Imagine the radial pressure on a unit of area, or /oj to be 
decomposed into two components/' and/^ figure 3, respect- 
ively perpendicular and parallel to the axial plane, O R\ 
along which rupture tends to occur; and consider but one 
quadrant of the bore at a time. 

Let cp be the variable angle made by the radial pressure 
with the plane O R', 

Then, /' =/o sin ^, 

and, since, 

d Z'=- R d cp^ 
J)' dZ=p(iR sm cpdcp = —p^Rd cos cp. 

n R 

Integrating between Z—^ and Z=— -— and the corre- 

<) 

spending values of cp^ viz. and 90°, and calling P^ the 
total pressure on the inner surface of the quadrant perpen- 
dicular to the plane of rupture, we have 



=/ 







XIX. — GUN CONSTRUCTION. 



And for the force acting on both quadrants to lift the semi- 
cylinder from the axial plane, or for the bw'sting effort 

%F=p,%R. (2) 

This might have been inferred from the fact that the burst- 
ing effort is independent of the configuration of the surface, 
upon which it acts. 
Eesistance. 

The bursting effort must be in equilibrium with the sum 
of the tangential stresses developed in both quadrants, or 
in figure 2. 

27'=/o2i? = 2^/=2 X areaierr'J?' 

or 



A=2--^-. (3) 



COROLLARIES. I 

1. The maximum permissible value of T\s the elastic limit 
of the material under tensile stress. Calling this and repre- 
senting by/g the corresponding powder pressure we have 

}.=e^. (4) 

Equation (4) gives the means of determining the maximum 
pressure for a gun of which the corresponding section is 
known, or of determining the thickness of which a gun of a 
given caliber should be made to resist a given pressure. 

2. If guns be similarly proportioned, R' •=znR^ whence 
by substitution 

/o=^^- (5) 



X13t.— CUJ^ C0N§TRt)Ctl6N. 



Equation (5) shows that all similar guns of the same material 
can resist the same maximum pressure. 

In the old cast-iron guns, in which for the reinforce, n was 
generally taken equal to 3, or the walls of the gun made 
one caliber thick, /o = f ^j i^ the metal be without internal 
strain. Chapter XV, page 21. 

3. Since < 1, A < 6^ unless i? = or ^' = oo . Or 

n 

the powder pressure must always be less than the elastic 
limit of the material. 

4. The curves of figure 4 are constructed from equation 1, 
using a constant value of ^'j= 6 and taking 7"= d and 
« = 3; 2; f respectively. It is apparent that as n dimin- 
lishes the curve T t; T^t^; T' t' becomes more nearly 
parallel to O R\ and the area beneath the curve tends to 
increase from this cause. On the other hand, this area tends 
to diminish from the decrease in the thickness of the wall 
of the gun in consequence of the increase in the radius of 
the bore: there is consequently some value of n which will 
make this area a maximum. 

To determine the value of n corresponding to a maximum 
area or resistance to bursting, denote this resistance by 6", 
and since it is equal to the maximum bursting effort we have 
from equations (2) and (4) 

Regarding R' as constant and differentiating we have 



7 C 

Whence, placing — ^ = we find 

R'= %R, or ;? = 2. 



XlX. — GUN CONSTRUCTION. 



That is to say, as shown by the following table, that when 
R' is fixed, if the thickness of the wall is one-half the caliber, 
the gun can withstand a greater bursting effort than with any 
other thickness. 

Table for R' = 6. 
n=S R=2 S' = ^d, 
n=2 R^S S" = ^ d = i S', 
« = f R= 4: S'" = id= S\ 

It is to be noted however, that since the bursting effort for 
one quadrant, or R, is equal to/„ Ry if/„ be kept constant, 
-P increases with R, so that, under ordinary circumstances, 
the thicker is the wall exposed to gas pressure, the greater by 
Equation (4) will be the value of /^. 

In order, as R increases, to diminish the value of the 
radial stress, we may form the gun of two or more con- 
centric cylinders. This has been done by boring out old cast- 
iron guns and lining them with a tube; since, for the same 
bursting effort, the pressure per unit of area on the cast-iron 
is diminished because the area pressed is increased. This 
will occur even if the material of the tube be of copper, the 
resistance of which may be neglected, and which may there- 
fore be supposed to act only by transmitting the pressure 
to the outside walls. 

Within limits the thicker is the tube and the greater its 
value of jE, the stronger will be the composite gun, since 
for a given stress on the exterior of the tube the less will 
be the strain on the adjacent walls, and, therefore, the 
smaller will be the maximum stress that the exterior wall 
will be called upon to bear. Conversely the power of such 
guns may be greatly increased. See /i, Chapter XI, p. 21. 

6. From the preceding corollary it follows that if a gun, 
the dimensions of which are fixed, be composed of several 



XIX. — GUN CONSTRUCTION. 



concentric cylinders, each one will be in the condition of 
maximum strength if its internal radius is half its external 
radius, or that the successive radii of contact will be in 
geometrical progressio7i. This, which is known as Gadolin s 
law^ is sometimes applied in modern gun construction. 



EQUALIZATION OF STRAINS. 

Preceding considerations show that owing to unequal 
distribution of the strains in a homogeneous gun, the 
strength of the gun increases much less rapidly than the 
thickness of the walls. 

The most favorable case would be when the whole thick- 
ness of the wall was under a uniform strain, since then the 
maximum pressure would be 

which would be n times greater than that given by equation 
(5). This result can be approximated to only by the sepa- 
rate or combined application of two plans commonly known 
as the methods of Varying Elasticity and of Initial Tension. 
These are actually however, but variations of the former 
principle. 

VARYING ELASTICITY. 

This consists in varying the elasticity of the concentric 
cylinders as explained in Chap. XV, page 11. The elasticity 
may be measured either by its coefficient or by its limit. 
This divides the subject into two heads. 

1. Varying Coefficient, or Rate E. 

Suppose the gun to be composed of two concentric cylin- 
ders, the tube containing the bore, and the jacket. If these 
are of the same material the stress transmitted to the jacket 



10 XTX. — GUN CONSTRUCTION. 

will follow Barlow's law. But if the jacket be made of a 
metal with E' > E, then the stress on its inner surface due 
to the strain arising from a given increase in the external 
diameter of the tube will be increased. For calling e the 
common strain, /, /, the corresponding stresses, and E^ E\ 
the coefficients of elasticity respectively of the tube and 
the jacket. 

If the value of E increase as r*, then the stress on the inner 
surface of the wall will he equal to that on the inner surface 
of the tube. 

For, let us call e^ the strain at the elastic limit of the 
tube, then 

8 
'^ = ^ 
At the outside of the tube the strain will be 

This will cause a stress on the inner wall of the jacket 
E'e J^ E' jR^ 

If now E : E' :: F? : R'\ E' R^ = ER'^ and t'= d. 

The thinner is the outside wall the less will the stress 
vary throughout its thickness, so passing to the limit we 
may say — That to develop an uniform resistance throughout a 
cylinder the coefficients of elasticity of the eleme7itary concetitric 
cylifiders must vary as the squares of their radii. 

This principle, though frequently referred to in gun con- 
struction, is now of little practical importance, since steel, 
the coefficient of elasticity of which is constant, and is 



XIX. — GUN CO^STRUCTION. 11 

greater than that of any other cannon metal, is now gen- 
erally employed for all portions of the gun. 

2. Varying Limit of Elasticity. 

Equation (1) shows that the stress on any cylinder is 
always greatest on its inner surface, and Equation (4) that 
for a given gun the value of p^ is limited by the elastic limit 
of the tube. 

Consequently, if the value of ^is constant, we may in- 
crease the strength of the gun by increasing the elastic limit 
of the tube. 

This may be done in three ways. 

a. By increasing the pt'ifuitive elastic limit hy varying the 
composition or structure of the tube. This is not practically 
done. 

b. By giving it a special elastic litnit before the bore is finished, 
viz. : 1st; by raising the elastic limit itself by preliminary ten- 
sion, as by mandrehng (Chap. XV, p. 22), or .by firing high 
proof charges. 2nd ; by lowering the origin of stresses by a 
preliminary compression, as by temporarily wrapping the tube 
with successive layers of wire until the surface of the bore 
receives a permanent set. 

c. The principle of initial tension consists in subjecting the 
interior cylinders to a stress of compression by the reciprocal 
extension of the outer cylinders. 

The effect is to increase the work required to deform the 
inner cylinders, in which the strains due to firing are the 
greatest, by diminishing the work required to deform the 
outer cylinders, in which the strains due to firing are the 
least. 

The foregoing explains the gain in strength by mandrel- 
ing, and also" why the heat of firing may really tend to 
strengthen a gun instead of to weaken it as is generally 



VZ XIX. — GUN CONSTRUCTION. 

supposed; since in both cases, the inner concentric cylinders 
being expanded more than those exterior to them, stresses 
are developed in the exterior cylinders which resist the further 
extension of the inner portions. 

It also explains the advantage of forming the tubes of more 
ductile material than the jacket and hoops, since if excessive 
powder pressure should expand the bore beyond its elastic 
limit, the initial tension developed outside would tend to 
prevent its further dilatation. 

It accounts for the former preference for bronze, the duc- 
tility of which sometimes caused such guns to fissure first 
on the outside, where it was unsupported, while, on the 
contrary, cast-iron would crack first on the surface of the 
bore where the danger would less readily be seen. 

Rodman's process of cooling cast-iron guns from the in- 
terior by a stream of water, while the exterior of the flask 
was heated by fires, was intended to utilize this principle 
and was the first instance of its application on a large scale. 
(Chap. XV, p. 21.) 

But, while the cooling of the exterior portions of the cast- 
ing might be retarded relatively to that of the portions next 
to the bore, it could not be postponed until all the interior 
portions had solidified. 

Consequently the state of rest of such a gun could be 
represented by figure 5 in which the dotted lines represent 
what was desired and the full line what was attained. The 
process was besides uncertain, since guns have been known 
to break spontaneously from internal stresses so developed. 

I APPLICATION TO BUILT UP GUNS. 

The results sought by Rodman may be attained much 
more certainly by the process of building up guns as ex- 
plained in Chapter XV. In such a gun if the tube be com- 



XIX. — GUN CONSTRUCTION. 13 

pressed until, under the law by which the stresses vary, the 
elastic limit of compression, p, be reached on the surface 
of the bore, then the effective value of the maximum tan- 
gential stress to which this surface may be safely exposed 
on firing will be 6 -\- p and the maximum safe pressure for 
the tube will approach as a limit 

J. = iS + p)'^. 

The effect of this pressure is shown in figure 6, in which 
the stress will change from — p to 4- ^ on the surface of 
the bore. If we take p= 6, as is commonly done, then the 
stress on the exterior of the tube will change from — ^' 7\ 
to -^jR^ T^ as shown. 

Now consider the jacket. The negative tension of the 
tube is due to a positive tension of the jacket resulting from 
shrinkage. Since the system is in equilibrium, the algebraic 
sum of the tensions on the tube and the jacket must be equal 
to 0; and, since from Barlow's law the tension, whether 
positive or negative, is always numerically greatest on the 
inner surface of a cylinder, we would have the condition 
represented by figure 6, in which the area 

RpT^R' = area R' T' T" R" . 

This represents the state of the system at rest. 

It is evident that the configuration of the stress area 
on the jacket, and therefore the maximum stress, R' T\ 
which it is called on to sustain from the shrinkage, will 
depend upon the thickness of the jacket. Also that R' T' 
must not only not exceed the elastic limit under tension, 6' ^ 
of the jacket, but must be so far beneath it as to admit of 
•the increment due to firing. 

Now suppose the system to be placed in action by the 
powder pressure and for simplicity assume that pz=: =.6', 



14 XIX. — GUN CONSTRUCTION. 

As the tension on the surface of the bore changes from 
— pto -\- 6 the strain on the surfaces of contact will increase 
the tension there by a quantity. 

For the tube this will simply change the sign of the stress 
from — to +. 

For the jacket the addition will be positive, the most 
favorable case being when the dimensions of the jacket are 
so chosen, as in figure 6, that the tension at rest + the 
tension in action = 6'. The state of the system in action 
is shown by the dotted lines of figure 6. 

The tangential resistance of the system will be propor- 
tional to the sum of the areas p R B T^ R' T^ p {=%s) 
+ R' T/ T,^ R" R' {= s') - R' T' T" R" R' (= s;) or 

:2 

:2 = 2^ + /-^, and/o= ^• 

The dimensions of figure 6 render such a gun about twice 
as strong as if it were a simple tube of the same size and 
elasticity. 

It is evident, that if, as on page 9, we suppose the gun 
to consist of an indefinite number of cylinders in which the 
initial tensions are properly applied, the thinner the cylinders 
are made, the less will be the difference of the tensions on 
their interior and exterior surfaces and the more nearly will 
the broken line d T, T/ r,, become parallel to O R" , or 
the more nearly will the resistance of the gun approach the 
ideal case. 

The difficulties of manufacture have generally limited the 
number of cylinders to less than 5 but these difficulties can 
be overcome by making the cylinders of continous wire 
wrapped around a central tube. 



XIX. — GUN CONSTRUCTION. 15 



SHRINKAGE. 

It is seen that the initial tension depends primarily on 
the shrinkage. In built up guns this may be due to heat- 
ing the exterior cylinder as described in Chap. XV, or to 
forcing by hydraulic pressure one cylinder within another, 
the contact surfaces being reciprocally conical, or by wind- 
ing wire continuously over a central tube. By whatever 
method the result may be attained, the stress on the contact 
surfaces is due to the strain resulting from the compression 
of the inner cylinder and the extension of the exterior. 

To determine the shrinkage required to produce a given 
initial compression without exceeding either p in the inner 
cylinders when the system is at rest or 6 in the exterior 
when the system is in action, is one of the principal objects 
of the different theories of gun construction now in vogue. 
A full discussion of these theories is not possible in this 
course, but the following treatment of the subject based 
upon Barlow's law illustrates the methods now employed. 

Let e, e' be the strains on the adjacent surfaces of the 
tube and jacket, for the corresponding stresses R' T^ = /, 
and R' T' == /' and let o* = <? + <?' be the shrinkage strain. 

/ t' 

Then since e— —=^ and e' = -=r , from note, page 21, 
jb JtL 

<T=-^ = ^{t+n or AJi'= 5 c+o- 

Consequently, as stated in Chapter XV, the tube would 
be turned to a diameter 

2R' 



(/ + +2^' 

and the jacket would be bored to its finished size. The 
effect of shrinkage would be to vary the radii somewhat from 



16 . XIX. — GUN CONSTRUCTION. 

those assumed, and to increase the length of the tube. 
These variations, which, for this discussion are not taken 
into account, afford one of the best means of testing the 
accuracy of the hypotheses upon which different theories of 
gun construction are based. 

LONGITUDINAL STRESS. 

This tends to "unbreech" a gun or to produce what is 
known as a "ring fracture," the plane of which approaches 
that of a right section. 

In homogeneous guns it was sufficiently resisted by the 
sections required to resist the tangential stress; but, in com- 
posite b. 1. guns, except so far as friction due to shrinkage 
and powder pressure may assist, that portion which contains 
the breech block has to support this stress independently of 
the portions which give tangential strength. 

The bursting effort is tt jR."^ p^. It tends to pull the piece 
apart, generally in rear of the trunnions to which it trans- 
mits the pressure causing recoil. Consequently the piece 
carrying the breech block must be firmly united to the 
trunnions. When b. 1, guns were first made the block was 
secured to the tube, but this arrangement, although theo- 
retically advantageous,* is no longer generally employed. It 
is thought that the radial expansion of the tube diminishes 
the bearing of the screw threads of the breech block, and 
that the tube is inclined to fissure through the screw threads. 

Supposing the longitudinal stress to vary through the 
cross-section, its resistance may be determined as follows : 

* From the analysis referred to on page 2, it follows that the longitu- 
dinal stress of the tube should develop a negative radial stress which 
would neutralize a portion of the powder pressure. This has been con- 
firmed by experiment on a small scale, and it is said that recent cannon 
made abroad have the block screwed into the tube. 



XIX. — GtJN CONSTRUCTIOK. 17 



The area of cross-section of an elementary cylinder whose 
radius is r and the thickness of which is dr will be ^Ttrdr. 
This will receive a variable stress q the intensity of which 
will vary with its distance from the axis, so that the resistance 
of the section whose internal and external radii are i?"and R' 

q%7trdr. 
n 

If we suppose q to vary by Barlow's law, we have 

Substituting this value of q and integrating we have for 
the total resistance 

^ J!L=27rie^^Nap.log— . 

Equating this with the bursting effort, we have for the 
condition of equilibrium 

A = 2 Nap. log ^. (6) 

In modern guns the ordinary values of 0, R' and R are 
such that the maximum value of /^ allowed by this equation 
is considerably greater than that allowed by their tangential 
resistance, so that these guns are abundantly strong against 
longitudinal stress. 

Equation (6) is useful for computing the pressures 
necessary to burst spherical shell for which purpose it gives 
results closely confirmed by practice. In such cases for B 
should be substituted the tenacity of the material. This is 
allowable since the ductility of such castings is small. 

WIRE-WOUND GUNS. 

The peculiar properties of cold drawn wire described in 
Chapter XV; the direction assumed by the fibers in the 
gun, and the increased facility of construction have for 



18 $Ct5t. — GtJN CONSTkUCtlOl^. 

many years made this material a favorite subject of study 
by gun makers. 

Until recently, however, the difficulty of providing suffi- 
cient longitudinal strength, and mechanical difficulties con- 
nected with the attachment of the ends of the wires have 
caused steel forgings to be preferred. 

The following may be named as devices intended to pro- 
vide the longitudinal resistance. 

Dr. Woodbridge, of New Jersey, the originator of the 
idea, proposed, after winding his tube to immerse the entire 
gun in a bath of melted bronze, so as to braze or solder the 
spirals and the layers together. This was found mechanic- 
ally impracticable and the bath, by annealing the wire, 
de&troyed much of its elasticity. Various experimenters 
have tried longitudinal bars or staves connecting the trun- 
nions with the breech, but so far as tried these are not 
believed to have given satisfaction; the objection appearing 
to consist in the difficulty of making all the bars resist 
equally, for otherwise they will tend to rupture in detail. 
Crozier's Wire Wound Gun. 

This gun, now under construction, is devised by Lieut. 
Crozier of the Ordnance Department. 

It consists — 

1. Of a thin steel tube forming a core for the winding; 
to contain the rifling and to prevent the erosion of the wire. 
It also incidentally gives longitudinal stiffness. 

2. Of wire, to give tangential strength. This is preferably 
of rectangular cross-section. Relying upon the support of the 
wire wrapping, it is intended to produce an initial preliminary 
compression considerably in excess of p. See page 11. For 
experimental purposes it is assumed that the relatively thin 
tube will withstand dilatation and contraction through a 
considerably greater range than 6 -\- p. 



XIX. — GUN CONSTRUCTION. 19 

The difficulties in attaching the wires have been success- 
fully overcome by electro-welding. According to the method 
proposed by Mr. Longridge of England each coil of wire is 
wrapped with a tension diminishing from within outwards, so 
that the tension of the inner layers will be eventually less 
diminished than if the tension of winding were constant. 

In such a gun, properly constructed, the tangential strain 
developed by firing will be uniform throughout the entire 
thickness of the walls. 

3. Of a steel cast jacket carrying the breech block at one 
end and the trunnions at the other and so furnishing the 
required longitudinal strength. It also gives longitudinal 
stiffness and being lightly shrunk on it also affords some 
tangential resistance. This, the heaviest unit of construc- 
tion is made, of cast steel on account of its cheapness, its 
radial distance and its adaptability to the present state of 
the arts in the United States. 

Practical Corrections. 

WEIGHT OF CANNON. 

The dimensiojis of cannon are sometimes increased be- 
yond what is required by their elastic strength so as to in- 
crease their weight and thereby diminish the destructive 
energy of their recoil; because, calling E this energy, and 
e that of the projectile at the muzzle, and the corresponding 
masses and velocities respectively J/, ;//, ?^and v^ we have 
from the equation of momenta, the general equation, 

8 a m 

M V =^ mv or MV=^mv or E^-^r-pe. (7) 

M ^ ^ 

Equation (7) is an important one to remember, particu- 
larly for small arms. 



20 XIX. — GUN CONSTRUCTION. 

This equation is not exact, since it neglects the momentum 
of the powder gases, (Chapter XI, page 18), but it is con- 
venient for general discussions. For a more exact formula 
see Chapter XXII. 

LINERS. 

In order to provide against the erosion of the bore, large 
built up cannon are sometimes lined for a short distance in 
ifront of the chamber with a thin tube which can be replaced 
with comparative facility. Guns which are properly de- 
signed appear more likely to fail from this cause than as 
the result of stress. 

LIMITS. 

It is not considered advisable to work up to the limits p 
and 6 as, for the sake of illustration, has been supposed. 
A safe margin is allowed in both cases. Indeed the inverse 
method is that generally followed, the gun being designed 
to safely resist a certain value of /<,. 

It can be shown theoretically that no great advantage is 
gained as to tangential strength by increasing the thickness 
of the walls over the powder chamber, much beyond one 
caliber. See General Remarks^ Appendix. 

gadolin's law. 

Owing to the practical difficulty of making perfect forgings 
of the thickness which this law would require for the exterior 
layers it is not generally observed. 



XTX. — GUN CONSTRUCTION. 21 




Note 1, Page 15. 



Let R^ be the exterior radius of the tube, and R^ the interior radius of 
the jacket before shrinkage ; and let R/ be their common radius after 
shrinkage. 

The effect of the shrinkage will be to diminish the radius of the tube 

Similarly, for the jacket e' = • ^ '-^ e, since / <; /''. 

The total shrinkage will be 

R^-R/ R/-R, 

R^ and R^ are so nearly equal to each other, and so large when compared 
with the numerators of the fractions that either R' or R^ may be used 
as a common denominator without material error. R' it taken because it 
pertains to the tube on which the excess is left as described in Chapter XV, 
The true shrinkage will therefore be slightly greater than 



22 XIX. GUN CONSTRUCTION. 



THE ELASTIC STRENGTH OF GUNS. 

By Captain L. L. Bkuff, U. S. Ordnance Department. 
The object of this discussion is to give a general idea of 
the methods employed in modern gun construction, for 
determining the strength of guns, the strains to which they 
may be safely subjected, and the methods by which the re- 
quisite strength may be obtained. 

Definitions. 

The elastic limit of a metal is the greatest load in lbs. per 
square inch of section which the metal will sustain before it 
acquires a permanent set. 

There are various elastic limits, such as those for tension, 
compression, torsion, etc., depending on the manner in which 
the stress is applied but the only ones of practical importance 
in gun construction are those for tension and compression. 

The modulus of elasticity of a metal (see Michie's Mechanics, 
art. 22), is the ratio of the load or stress in pounds per square 
inch, to the elongation or strain per linear inch produced by 
this load within the elastic limit. It is expressed by dividing 
the stress by the strain. Since within the elastic limit the 
strain or elongation is proportional to the stress or load, it is 
evident that this ratio is constant for the same metal. Its 
value for all gun steel is taken at 30,000,000 lbs. 

As in the case of the elastic hmit, there are various moduli 
of elasticity, as for tension, compression, etc., but those for 
tension and compression, which are the only ones used, agree 
so nearly, that the uniform value given above is assumed for 
both. 

Hooke's Law. — This law is expressed above. It is as 
follows : Within the elastic hmit of a metal, the stress is pro- 
portional to the strain. 

Stress and Strain. — In the discussion stress will be used to 
denote the force in pounds per square inch producing a given 



^13^. — GUN CONSTRUCTION. 2^ 



extension or compression per linear inch, and strain the corres- 
ponding elongation or compression produced by the stress. 

General Principles. 

The construction of the modern gun is supposed to be 
understood. That is, that it is composed of an interior tube, 
surrounded by a jacket and one or more rows of hoops. 
That the jacket carries the breech-closing device, and that 
the jacket and hoops have interior diameters which are less than 
the exterior diameters of the parts they envelop, by a certain 
prescribed amount, and that the difference in diameter between 
the enveloping cylinder and the enveloped cylinder is called 
the shrinkage. In order to place the smaller or enveloping 
cylinders over the enveloped cylinders, the former are ex- 
panded by heat till they will pass over the corresponding sur- 
faces, when they are cooled in place by the application of 
water. 

Theory. 

The principle of initial tension is employed in the modern 
built up gun. The interior layers which are under the greatest 
strain, due to the action of the powder gas, are compressed 
by the exterior layers, jacket and hoops. When the pressure 
of the gas acts upon these interior layers, it has first to over- 
come this initial compression, and then to extend or compress 
these layers until they reach their elastic limit for extension or- 
compression, before the maximum resistance of the gun is 
reached. The exterior layers are subjected to initial tension, 
by which their capacity for resisting interior pressure is partly 
diminished, but owing to the law of its transmission, the strain 
upon them is so much less per square inch than it is upon the 
interior layers that they are able to resist it. Thus the interior 
layers are relieved of a portion of the strain, due to the action 
of the powder gas, and the strain transmitted to the exterior 
layers, by the modern process of gun construction. 



24 XlX. — GUN CONSTRUCTION. 



The best condition for strength in a gun is when every 
layer of metal in its cross section is strained equally by a given 
stress or pressure. 

The foundation of the theory of the built up gun is 
this. That ifi whatever state the gun may be considered^ 
whether under the pressure of the powder gas, or free from it, 
7ione of the fibers of any cylinder in the gim shall be elongated 
or contracted beyond the elastic lifnit of the metal of that 
cylinder^ which elastic limit is determined by the test of the 
metal in a testing machine. 

Two states or conditions of the gun are considered in this 
discussion ; one, called " the system in action," which means 
that the gun is subjected to the maximum interior pressure 
which it can support with safety, and the other, called " the 
system at rest," that is, when the gun is free from the pressure 
of the powder gas, although the strains due to the shrinkages 
still exist. 

Methods of Discussion. 

The general method of discussion is : 

First. To assume a cube of metal the length of whose 
edges is unity, and which is supposed to be perfectly elastic 
up to a given limit ; to deduce the equations of equilibrium 
which show the relations between the forces acting upon this 
cube in directions at right angles to its faces, and the corres- 
ponding elongations and contractions produced by them. 

Second. To transform these equations so that they will apply 
to the elements of a cylinder of metal ; or in other words, to 
deduce the equations which give the relations between the 
stresses at different points throughout the right section of a 
single cylinder. 

Third. To pass from a single cyhnder to a compound 
cylinder composed of any number of single cylinders, and to 
deduce for the latter the compressions and extensions pro- 



XIX.— GUN CONSTRUCTION. 25 

duced by given pressures, and the shrinkages or differences 
of diameter which will produce given compressions and 
pressures. 

FIRST. — EQUATIONS OF EQUILIBRIUM FOR A CUBE OF METAL 
OF CONSTANT ELASTICITY WHOSE EDGES ARE EQUAL TO 
UNITY. 

It has been found by experiment, that when a cubical elastic 
solid is acted upon by a given force of extension or com- 
pression in a direction perpendicular to two of its opposite 
faces, this force produces an extension or a compression of 
the cube in the direction of the force, of a given amount, and 
a corresponding compression or extension in the two direc- 
tions at right angles to the given force equal to one-third 
the first extension or compression. 

The force is supposed to be within the elastic Umit of the 
solid. 

For example, suppose a force of extension /*, Fig. 7, to act 
upon the opposite faces of a cube of metal, whose edges are 
each one inch long. If it extends the edges a a a ^^ of a.n 
inch it will shorten the edges d I? d and c c c ^ of ^^ :=: ^ oi 
an inch, and the same for any other force. 

In figure 8 
Let B = the modulus of elasticity of the cube. 

X, V and Z= three forces acting at right angles to the 

faces of the cube, being tensions in the figure. 
X; fi; V, =z the extensions produced by the three forces 
Xy Fand Z, respectively. 

Then the force X, according to the preceding principle, 
produces an elongation in its own direction equal to 

But the force K diminishes this elongation by the amount 

iZ 



26 XIX — GUN CONSTRUCTION. 

and the force Z by the amount 

Hence the total elongation in the direction of X is 

In the same way we have for the total elongations in the 
directions of Kand Z 



'=4{-f-^) 



These three equations express the relations between the 
elongations of the faces of an elastic cube whose edges are 
unity, and the corresponding forces acting on them. 

SECOND. APPLICATION TO AN ELASTIC CYLINDER. 

We have supposed the three forces to be tensions. In the 
case of a gun cylinder, however^ two of the forces are ten- 
sions, one acting in the direction of a tangent to the cylinder, 
and the other parallel to the axis, while the third is a pressure 
and acts in the direction of the radius. In Figure 9, let / = 
the radial pressure, / = the tangential tension, ^ the longitu- 
dinal tension, per unit of area. 

Substitute / for X, — J> for Y since it acts opposite to F, 
and ^ for Z, and the above equations become 



} 



'--M' + T + l)) W 



XIX. — GUN CONSTRUCTION. 27 

The first of these equations expresses the total change per 
unit of length in the direction of the tangent of the cyhnder ; 
the second the total compression (being negative) in the 
direction of the radius ; and the third the total change in the 
direction of the axis, due to the three forces /, / and q. 

In order to apply these equations in practice the changes of 
dimensions must be expressed in terms of the radii of the 
cylinder and of the forces acting upon it. To express the 
equations in these terms we proceed as follows : 

Equations of Equilibrium in Terms of the Radii of the 
Cylinder. 

Let Figure 10 represent a section of the cylinder perpen- 
dicular to the axis. 
Let R = interior radius. 
R ' n: exterior radius. 
r = the radius of any circle of the section. 
r' = any other radius exterior to r. 
p zzzthe radial pressure per unit of surface at the distance 

r from the axis. 
tz=. the tangential stress per unit of surface at r, 
q = the stress per unit of section parallel to the axis of 
the cylinder, and supposed uniform throughout the 
section. 
/*=the interior radial pressure per unit of surface, 

being the value of / for R. 
^'^the exterior radial pressure per unit of surface, 

being the value of / for R' . 
T and T' = the values of / for r = Rj and r= i?' re- 
spectively. 
^=the modulus of elasticity. 
The pressure/, whether acting inward or outward, develops 
in the direction perpendicular to A B, Figure 10, a force 
equal to 2j>r. 



28 XIX. — GUN CONSTRUCTION. 

Increase r to r', and represent by f the new value of/. 
This develops a force in the direction perpendicular \.q A B 
equal to 2 p' r* . The algebraic difference between these forces 
is in equilibrio with the product of twice the thickness of the 
ring r* — ;' into the mean stress throughout the ring, which 
represent by r. Hence 

2/ / _ 2 /r = — 2 T (^ — r) 

dividing 

P'r' —pr _ ^ 
r* — r 

passing to the limit of the ratio in the first member by making 

d{pf) 



( p' r' —pr \ 



limit of 1 , ^ 

r' ^ 



limit of 

\> 
Hence 

d (pr) __ 



Taking the last of Equations (8), which expresses the strain 
in the direction of the axis of the cylinder, and supposing 
this uniform throughout the cross-section, we have 

P\ 



^=M' 



i+8 



From this we have 



or t— p=^^{q— V E) (10) 

But the second member of this last equation is constant, 
since we have supposed v uniform throughout the section ; 
hence 

/ — / = constant. 



XIX. GUN CONSTRUCTION. 29 

From which we may unite 

t—p= T—P (A) 

t—p=T' — F' (V) 

From Equation (10) we have 

t=P + i(q-vE) (11) 

Substituting this for / in Equation (9) we have 

performing the differentiation as indicated ; / and r being 

variable, 

pdr + rdp ^ o / Z7\ 

Jr = — / — 3(^— v^) 

reducing 

dr dp 



r ~~ 2 / + 3 (^ — V ^) 
Integrating 

log= (y) = 4 log. (2/ H- 3 (? - V ^ + log. C 

i- = ^(2/ + 3(?-r^)) 
Substituting the value of/ + 3 (? — v E) from (11) we have 

! = .(/+/) 

(/ -j- /) r' = — = constant 
From which we can write 

{t^- p)r' = {T-^P)R' (Q 

{t-\- p)r' = {T' -\-P<)R''' {D) 

From Equations (A) and (B) we derive the following 
principle : 

The difference between the tension and the 'Pressure is the 
same at all points. 



30 XIX. — GUN CONSTRUCTION. 

From (C) and {D) we have the following principle : 

At any point whatever^ the sum of the tension in the direction 
of the circumference, ajid of the pressure in the direction of 
the radius, varies inversely as the square of the radius. 

This demonstration is given by Captain Crozier, Ordnance 
Department, in " Notes on the Construction of Ordnance," 
No. 35. 

Applications. — It has been shown by Captain Birnie, Ord- 
nance Department, that in considering the radial and tangential 
strains in a gun cylinder, we may, without appreciable error, 
omit the longitudinal strain, or the strain parallel to the axis, 
and afterwards consider this latter strain separately. This 
conclusion has been proved to be correct, by actual measure- 
ments of guns during construction. This is equivalent to 
making in Equation (8) 

q^o, 
when the equations become 

In the last equation, which gives the change in the longi- 
tudinal direction, this change will be produced by/ and /only. 
From Equations (C) and {D) we have 

(5-/ -j- pi) Ri 2 ^ (r-l. p) j^^ 

and from {A) and {B) 

T' — F' = T—F 
Combining these two equations and ehminating T' we 

have 

■ F'^ + J^ 2 F' ' F' 
^ ^' F'^ — F*" F" — F" 



/ = 



XI3^. — GUN CONSTRUCTION. 31 

Substituting this value in (J) and (C), combining the re- 
sulting equations, and eliminating/ we have 

Ri^ — R' -I- ^,2_^. ^ (13) 

And by combining and eHminating / between the same 
equations we have. 

_ FJ ^ — P' Ii'\ . J^'^^'iP—P') 1 

Substituting these values of / and / in Equations (12) we 
have 

2 {PR' — P' R'^) q^R'^ R' i^P— P') 1 
'^ "" $(R" — R')jS "f" 3{R'' — R')£ r" ^^^ 

_ ^(PR"— P' R'"") 4tR" R' {P—P') 1_ 
^— d(R'^ — R')£ ~" S {R' ' — R') E r" (^^^ 

_ ^{PR' — P'R'') 
^ — "" 8 (i?"* — R') E vA ') 

These equations give the values of the elongations or con- 
tractions in terms of the pressures and radii, and the known 
modulus E^ for any radius r. 

Elastic Strength of a Simple or Single Cylinder. 

Now it may be shown that the greatest elongations and 
compressions of the fibres of a cyUnder subjected to an interior 
pressure P, and an exterior pressure P' , take place at the inner 
surface of the cylinder. (See appendix, Note 35, on the Con- 
struction of Ordnance.) Assuming this, we recur now to the 
fundamental principle stated above "that no fibre of any 
cylinder in the gun shall be elongated or contracted beyond 
the elastic limit of the metal of that cylinder." 

Let Q = the elastic limit for tension, 

p = the elastic limit for compression in pounds or tons 
per square inch, of the cylinder. 



82 XlX. — GUN CONSTRUCTION. 



Then the extension and compression at the elastic Hmit will 
be respectively 

and by the above principle these must be equal to the greatest 
values of /I and [z respectively. 

Since the greatest extensions and compressions will occur 
at the interior of the cylinder, we have for their greatest 
values by substituting jR for r in (15) and (16) 



3 (i?' ' — R') E 



(18) 



f^ — — 3 (i?' » — R'YE (^^) 

Placing these equal to -^ and -^ respectively, we have 
. (4:R" + 2R')P—6R" P' 



d(R'' — R') 



I 2 pt 



___ (^R'^ — 2R')P—'2R'''P 
P— 3(R'' — R') 

From which we find two values for P, viz. : 
■^ 4 i?' ^ + 2 ^^ 

^ — 4: R" — '2.R' 



(20) 



(21) 



Equation (20) gives the value for the interior pressure, 
which will cause the layer of metal on the interior of the 
cylinder to reach its elastic limit by extension, and Equation 
(21) the value which will cause the same layer to be com- 
pressed to its elastic limit ; these pressures being in pounds 
or tons per square inch according as d and p are expressed in 
pounds or tons. 



XIX. — GUN CONSTRUCTION. 83 

It must be remembered that the less of the two pressures, 
measures the elastic strength of the cyHnder. 

THIRD. — THE ELASTIC STRENGTH OF A COMPOUND CYLINDER, 
OR OF A BUILT-UP GUN. 

For the sake of clearness in the nomenclature, and of sim- 
plicity in discussion, the gun will be supposed to consist of two 
cylinders only, shrunk one upon the other, and the resistance 
of this compound cylinder, and the shrinkages to be used in 
its construction, will be deduced. 
In figure 11 let 

P^ = the maximum internal pressure to which the 

gun can be subjected. 
P^ ■=. the normal pressure at the surface of contact 

of the two cylinders. 
P^ •=. the exterior normal pressure. 

A' Pv P-i ^^ variations in the pressures, P^^ P^ and P^ due 

to any cause whatever. 
The above pressures and variations of pressure are those 
which exist with the " system in action," — that is when the 
maximum gas pressure is acting on the bore. 
Let 

PI = the normal pressure acting at the surface of 

contact of the two cylinders when the system 

is at rest — that is, when the pressure of the 

gas does not act on the bore. 

// = the variation of P^ due to any cause whatever. 

J?g, i?j, R^ = the radii of bore, of interior of second cylinder, 

and of exterior of second cylinder respectively. 

0„, 0j =: elastic limits of inner and outer cylinders for 

extension. 
p^, pj = elastic limit of same for compression. 
E^, E^ = moduli of elasticity of metal of cylinders. 



34 XIX. — GUN CONSTRUCTION. 



Writing Equations (20) and (21) we have 

^ - 4^'^ + 2i?^~ ^^ 

^ — 4^'" — 2i?^ ^^^ 

Now it will be remembered that in the case of a single 
cylinder, Equation (20) gives the value of Z*^^^, the interior 
pressure which will cause the layer of metal on the interior 
of the cylinder to reach its elastic limit by extension, and 
Equation (21) the value of P^^ the interior pressure which 
will cause the same layer to be compressed to its elastic limit. 

Taking the outer or second cylinder of the gun, it is always 
under a strain of extension both in action and at rest, and 
hence Equation (21) will not apply to it. 

Equation (20) must therefore be used. To apply it to the 
present case, R and R' in (20) are the inner and outer radii, 
which now become R^ and R^ respectively. /*is the interior 
pressure, and it now becomes P^, P' is the exterior pressure, 
and it becomes P^. But this exterior pressure on the second 
cylinder is simply that due to the atmosphere, and it is so 
small in comparison with the other pressures considered that 
it may be neglected. Hence 

P. — o. 

Also Q becomes Q^. Making these substitutions in (20) we 
have 

_ %{R^-R^)Q, 
' ~ 4: Rl + 2 R,' 

This gives the value of the interior pressure on the outer 
cylinder which will cause its inner layer to be strained to the 
elastic limit for tension, and as this value is expressed in 



XIX. — GUN CONSTRUCTION. 85 

known terms, P^ can be readily calculated. The value of 0^ 
is obtained from test of the metal in a testing machine. 

Now taking the inner cylinder, the pressure P^ just found, acts 
not only on the interior of the outer cylinder, but also on the 
exterior of this inner cylinder. Hence one of the normal 
pressures acting on this inner cylinder is known, and we have 
to calculate the other. • 

This inner cylinder is not only extended by the action of 
the powder gas, but it is also compressed radially by this 
pressure, and it is subjected to a strain of compression by the 
force P^ which we have just found. In other words the inner 
cylinder is subjected to both tension and compression, and 
hence it is necessary to calculate both strains, and to take the 
smaller as the limit of its elastic resistance. 

Referring to Equations (20) and (21) the following changes 
must be made to apply them to the inner cylinder — 

P becomes P^ 

P' " P^ 

R " R, 

R' '* R^ 

e - 6^ 

Making these substitutions we can write 

,, 3{R,^-Rl) e,+ 6R,-'P, 
V 4:R,' + 2 Rl 

» ~ 4:R,^ ^2Rl 

Substituting in these equations the known values of the 
radii, and of ^^ and p^ together with the value of P, just cal- 
culated, we obtain two values for /*„, the smaller of which is 
the limiting value of the pressure for the compound cylinder 
under discussion. 



86 XIX. — GUN CONSTRUCTION. 



For convenience of reference these equations are collected 
here — 

p ^ 3 (i?i - R,' ) e, 

4 7?^ + 2 R,' 

^ (n _ 3(^.'-^a K^ ^^.'P. V (22) 

•^o ~ 4i?,^ + 2J?,1 ^ ^ ^ 

3 {R, - i?^) p„ + 2 i?,' -P. 



p(2) _ 



The values of P, obtained from Equations (22), are the 
pressures which will cause the interior of each cylinder to 
reach its elastic limit for extension or compression; and since 
the greatest strains in a cyHnder occur at its interior surface, 
and since also no part of any cylinder must be strained be- 
yond its elastic limit, it is evident that the values of P, thus 
obtained, represent the greatest strains to which the cylinders 
can be subjected. It will be seen hereafter, that these values 
cannot always be used in practice, since the bore in the state 
of rest, may be compressed beyond its elastic limit, by the use 
of these values. 

It is, therefore, necessary now to consider 

The System at Rest. 

Equations (22) give the pressures acting for the sys- 
tem when under the maximum pressure of the powder 
gas. It is evident, however, that when the system is at 
rest, great pressures will exist at the surface of contact of 
the two cylinders, due to the shrinkage of one on the other. 
These pressures generally increase from the exterior to the in- 
terior, and the interior of the bore is generally compressed 
from this cause to a greater degree than any other part of the 
gun. This compression of the bore may be so great as to 
exceed the elastic limit for compression of the metal of the 
inner cyHnder, and thus, although the gun is properly calcu- 
lated for action, the principle upon which the whole structure 



XIX. — GUN CONSTRUCTION. 37 

is built may be violated, when the gas pressure is removed. 
In this case", the elasticity of the tube is destroyed., as effect- 
ively as if by the powder pressure. 

It is evident, also, that when the powder pressure ceases, 
the pressure which existed at the surface of contact of the two 
cyhnders will change, and will assume some other value for 
the state of rest. The value of this variation of pressure at 
the surface of contact has been denoted by /, and at the sur- 
face of the bore by /o- The value of the pressure at the sur- 
face of contact for the state of rest has been represented 
by P\ 

Now it is evident that the difference between the pressure 
in action and at rest for any surface, gives the variation in the 
pressure at that surface. Hence, since the pressure at the in- 
terior of the bore, when the system is at rest, is zero, we have 

and also 

When these changes of pressure occur, they are accompanied 
by corresponding changes of dimensions of the surfaces at 
which they act, and these changes of dimensions depend 
directly upon the variations of pressure. The greatest changes 
of dimensions occur in the direction of the circumference or 
of the tangent to the surfaces, and Equation (18) gives the 
value of these changes for the interior surfaces. 

To Calculate these Changes of Dimensions. 

The variation of pressure acting on the outer cylinder .s 
/,, and the exterior pressure is zero, being that of tlie atmos- 
phere. Hence, substituting in Equation (18) for P its value 

p^ and making 

/" = o 
R -^ R, 
R' ^ R, 
E =^ E, 



38 XIX. — GUN CONSTRUCTION. 



we can write 



^^(4^^ + 2i?r)A 



3 (J^l — R:^) E, 

This represents the change of dimensions of the interior 
of the outer cyUnder per unit of length of circumference, 
under the change of pressure represented by p^. 

To find the change of the exterior of the tube due to the 
variations of pressures p^ and /, which act on it, we recur to 
the general Equation (15), which gives the change in the 
direction of the circumference, or of the tangent, of any 
cylinder whose exterior and interior radii are R' and R at the 
distance r from the axis. Replacing r by R' since the change 
at the exterior of the cyHnder is now required, we have 

_ %R^P-{^R^ + ^R'^)P' 
^ - 'i{R''^-R^)E ^^^^ 

To apply this to the inner cylinder now under discussion 
make 

R' = Ry 

and we write 

6 Rl A. - (4 Rl + 2 R,') A . 



A-= 



3 {R,^ - Rf) E, 



for the value of the change of exterior of inner cylinder or 
tube. 

Now since the outer surface of the tube, and the inner 
surface of the outer cylinder are in contact, the same change 
of dimensions must occur in both, at this surface of contact, 
and hence the two values of X obtained above are equal. 



XIX. — GUN CONSTRUCTION. 89 

We have therefore 

6 RIP, — (4 i?^ + 2 R^)p, (4 i?l + 2 R^) /, 



/i = 



Solving this equation with reference to p, we have 
QR,E,[Ri-R,']p^ 



E, {R,—Rn (4i^o + ^Rn + E,(J^,^ — J^t) (4^^ + 2 R,') 

(24) 
Now in this equation /„ is known, since it is equal to — P^ 
as before shown, and R^ has been already calculated by- 
Equations (22), hence we can calculate/,. 

Limiting Value for the Exterior Pressure on the Inner Cyl- 
inder, System at Rest. 

It has been stated that R^, given by Equations (22) represents 
the maximum stress to which the gun can be subjected in 
action, the smaller of the two values of P^ being used. It is 
necessary now to determine what value can be allowed for 
the exterior pressure upon the inner cylinder at rest, so that 
the interior surface of the latter will not be compressed by it 
beyond its elastic hmit. To do this we must find the value 
of Ri for the state of rest. 

The value of R/ for this state is as has been shown 

R/ =R. + Pi 

Assuming Equation (18) and making P — o^ since the 
interior pressure at rest is zero, we have 

~2 R"" P' 

A — 



{R^ — P')E 



which shows since it is negative, that there is tangential com- 
pression, and as this is generally greater than the radial com- 
pression. Equation (18) only is used. 

This compression must not exceed that at the elastic hmit 



40 XIX. — GUN CONSTRUCTION. 



which is 

P 

E 
hence we have 

for the limiting value of the compression at the interior of the 
inner cylinder. Changing the letters to correspond to the 
case of the tube under discussion ; that is, making 

F' = P/ 

R' ^ R, 

R ^ R, 

E ^E, 

P = Po 

and omitting the negative sign, as that simply indicates com- 
pression, we write 

2 R,' r/ p. 



or 

but 
hence 



(y?.' - K) E^ E, 



^, ^ (i?,' - F?^ p. 



2/C 
^ = ^. + A 



/>/=/». + /. ^ ^^-'^"5^° (25) 

and this value of P^ must not be exceeded. 

This equation gives the value of /*/ r= P^ -(" A i^^ known 
terms. 

But we have the value of /i from Equation (24) by substi- 
tuting for /„ its value — P^. Hence, substituting the value 
of /i from Equation (24) in (25), we obtain a new value for 
P^ which will cause the interior of the inner cylinder to be 
compressed to its elastic limit at rest. The value thus ob- 



XIX. — aUN CONStRUCTlOl^. 41 

tained for P^ must be substituted in that one of Equations 
(22) which gives the least value for P^. The new value thus 
obtained for P^ will be such that the inner cylinder will not 
be strained beyond its elastic Hmit either in action or at rest, 
and it represents the greatest value of the stress to which the 
gun can be subjected without exceeding the elastic limit of 
the metal composing it. 

THE SHRINKAGE. 

In Fig. 12, let OA represent the interior, and OB the ex- 
terior radius of the inner cylinder, and OC and OD the inte- 
rior and exterior radii of the outer cylinder, before they are 
assembled to form the gun. Then the length CJS= OB — OC 
is the shrinkage. As diameters are usually employed instead 
of radii in tables of shrinkages, a more usual expression for 
the shrinkage is 

2 C^ = 2 {OB — OC) 

or, in other words, the shrinkage is the difference of diameters 
of the enveloping and enveloped cylinders. This is called 
the absolute or actual shrinkage. The relative shrinkage is 
the shrinkage per unit of diameter, or per unit of radius, and 
is expressed by dividing the absolute shrinkage by the interior 
diameter of the outer or enveloping cyUnder. Thus the rela- 
tive shrinkage in this case is 

2CB ^ '^(OB— OC) CB 
^0C~ 2 0C ~ OC 

To determine the shrinkage for the case under discussion. In 
Fig. 12, let OA, OB, OC and OD represent the same quan- 
tities as above. 

Now, when the outer cylinder is heated and expanded till 
its interior radius OC is slightly greater than the exterior ra- 
dius OB of the inner cylinder, and the exterior cylinder while 
hot is placed on the interior cylinder, so as to envelop it, and 



4^ XIX. — GUN CONSTRUCTlOM. 

is then cooled in this position, it is evident that the outer cyl- 
inder will compress the exterior of the inner one, and that 
their surface of contact will assume some such position as 
K E E''y the outer radius O B oi the tube being compressed 
to O E^ and the inner radius O C oi the outer cylinder being 
extended to O E, Hence the radius O B has been compressed 
by the amount 

OB — OE z= BE 

and the radius OC has been extended by 

OE— 0C=^ CE ' 

and the sum of these two is equal to the original shrinkage, 

BC, or 

BE -^ CE^ BC, 

Hence, if we can find the values of the two quantities BE 
and CE^ we will have that of the shrinkage. 

Now when the two cylinders are assembled, and the system 
is at rest, we have found that the pressure P^ acts at the con- 
tact surface of the cylinders. That is, the exterior cylinder is 
acted upon by a force represented by P^, and this force pro- 
duces an extension per unit of radius of 

CE 

OC 

CE being unknown. But Equation (18) gives the value of 

this extension in terms of the radii, pressures and modulus of 

the cylinder. Remembering that 

P' = P^ — o 
P =P,' 
R' = R, 
R = R, 
E =E, 
we write 

CE _ (4 ^^ + 2 R,') P! 

OC ~ 3 {Rl ~ R^')E, 

This gives CE, 



XIX. GUN CONSTRUCTION. 43 

To find BEy or the compression of the exterior of the tube. 
The pressure acting is P/, as before, the interior pressure 
being zero. This change being at the exterior of the cyHnder, 
we use Equation (23), making the following changes, 

P = o 

P' = P^ 



Hence we have 


E =E, 


oc ~ ■^ - 


(4 iP„ + 2 J?,') P! 
- 3 {R;- - Rl) E, 



Strictly speaking, the true value is -—- for the change per 

unit of radius, but the difference between OB and OC '\s so 
small in practice that either may be used without appreciable 
error. 

Now it will be observed that the value of -^ = A just ob- 

tained, is negative, indicating compression, and this is evi- 
dently correct. 

But the shrinkage sought is the sum of two positive quan- 
tities 

BE 4- CE CB 
'OC ~ ~0C 
In order to avoid the negative sign, and obtain the quantity 

BE 

j^ under a positive form, we suppose that the exterior cyl- 

inder is removed from the interior cylinder. In this case it 
is evident that the exterior surface of the inner cylinder will 
expand and regain its original diameter, and that this expan- 
sion is exactly the same in amount as the compression BE, 
which was produced by shrinking on the outer cylinder. 
This is equivalent to supposing the pressure P^' neutralized 



44 XIX. — GUN CONSTRUCTION-. 



by an equal and opposite pressure ; that is, in the value of 

BE 

--T. we make 

P.' = - A' 
and that value becomes accordingly — 

BE _ (4 R^ + 2 R^) F,' 

a positive quantity. Now denoting by op the shrinkage of 
the two cylinders, we have 

CE-\.BE (4^/ + 2i?.^)P/ (4.R:-^<2R,^)P' 
^ OC ~ ^ (R^' — R:') E,~^S (R,' — R^') E^ ^ ^ 

In using this equation it must be remembered that cp is the 
relative shrinkage, or the shrinkage per unit of diameter. To 
obtain the absolute shrinkage, the relative shrinkage must be 
multiplied by the diameter. That is, if Z> represent the diam- 
eter and (p the relative shrinkage (both in inches), and *S the 
absolute shrinkage, then, 

S ^ (j)X z> 

and the exterior diameter of the cylinder must be made 
E>' = D-{- S 
Referring to figure 12, 

2 OC^ jD 
2CR=S=q)XZ> 
2 0B= D' 

GENERAL REMARKS. 

It can be shown theoretically that the maximum resistance 
is obtained from a gun cylinder when the radii of the differ- 
ent cylinders composing it, vary from the interior in geomet- 
rical progression. 



XIX. — GUN CONSTRUCTION. 



45 



This, however, is never adopted in practice for various 
reasons, one of the principal being the objection to very thick 
cylinders on account of their being more difficult to forge, 
less uniform in quality, and more liable to imperfections in 
the metal. 

It can also be shown that no great advantage is gained as 
regards tangential strength, by increasing the thickness of the 
walls of the gun over the powder chamber much beyond one 
caliber. These considerations combined with the capacity of 
the forging plant where hoops, tubes and jackets are made, 
will serve to fix the limits of thickness of the different cylin- 
ders composing the gun. Examples are given here of three 
modern guns : 



Gun. 


Diam. of 
powder 
chamber. 


Thick- 
ness of 
tube. 


Thick- 
ness of 
jacket. 


Thick- 
ness of 
-Whoops. 


Thick- 
ness of 
£ hoops. 


Total 
thickness 
of wall. 


Total 

thickness 

of wall. 




Inches. 


Inches. 


Inches. 


Inches. 


Inches. 


Inches. 


Calibers. 


8-in. 


9.50 


2.75 


4.25 


3.30 




10.30 


1.0842 


10-in. 


11.80 


3.20 


4.90 


2.525 


3.10 


13.725 


1.1631 


12-in. 


14.20 


3.90 


5.80 


2.90 


3.425 


16.025 


1.1285 



The caliber being the diameter of the powder chamber, 
the above table shows that the thickness of wall only sHghtly 
exceeds one calibre. 

Having determined from the above considerations the 
radii of the different cylinders composing the gun, the values 
of the pressures which the gun will support in action may 
be calculated from Equations (22), B and p being known 
from tests of the metal in a testing machine. 

Having obtained the values of /{ and F^ from Equations 
(22), the system must be considered at rest, and the values 
of the pressure P/ deduced which will be safe for that state 
of the system. This is given by Equation (25). 

Then this value of P^' must be used to deduce a new 



46 XIX. — GUN CONSTRUCTION. 



value of Z*! , and this value of P^ must be substituted in that 
one of Equations (22) which gave the lower value for P^ . 
The new value of P^ thus deduced will represent the maxi- 
mum pressure to which the gun can be safely subjected. 

We can now calculate the shrinkage from Equation (26), 
using the value of P/ already found. 

The same method can be extended to guns composed of 
any number of cylinders, but the subject becomes more 
complex as the number of cyhnders increases. 

After calculating the shrinkages, the same fundamental 
formulas may be used to calculate the compressions of the 
bore produced by the assembhng of the cylinders. The 
results of these calculations are then compared with actual 
measurements of the bore made during the assembling of the 
gun, and the agreement is in every case found to be 
remarkably close, and furnishes a proof of the correctness 
of the theory. 



Thickness of Gun at Different Points. 

The thickness of the gun at the reinforce is determined by 
the considerations already given, and as stated, rarely 
exceeds one and a half calibres. To determine its thickness 
at various points along the chase, it is necessary to have the 
'* pressure curve " of the powder at different points along the 
bore. Formulas have been deduced for this curve by various 
authors, but it is not deemed necessary to give them here. 
The results obtained from them do not agree, and recent 
experiments on a small gun show that Noble & Abel's formula, 
Chapter IX, agrees very well with the results of experiment. 
Using this formula, the pressure curve can be obtained. 

The elastic resistance of the gun, or the values of P^ for 
different sections of the gun, are calculated as explamed, and 
plotted, and the curve of powder pressure for the same gun 



XIX.— GUN CONSTRUCTION. 47 

is also plotted to the same scale. The curve of resistance 
should always He above the curve of pressures. 

Length of Gun. 

This may be determined for a given initial velocity and 
given conditions of loading, charge of powder, etc., by 
Sarrau's formulas for velocity, but as a practical rule, it may 
be stated that at present the total length of modern high 
power guns varies between 35 and 45 calibres, and that the 
tendency is toward the higher limit. 



XX. — EXTERIOR BALLISTICS. 



CHAPTER XX. 

EXTERIOR BALLISTICS. 

This treats of the motion of the projectile after it has 
left the gun. 
Definitions. 

The sights are two projections on the upper surface of 
the piece, the distance between which parallel to the axis, 
is called the sight radius^ or sometimes the radius of the 
gun. 

Each sight contains a definite point called the sight point. 
That for the front sight, which is fixed, is generally deter- 
mined by the intersection, at an acute angle, of the faces 
of a wedge or by the intersection of cross wires as in sur- 
veying instruments. That for the rear sight consists of a 
notch in a bar, or a pin hole. 

The rear sight point is movable so as to vary its distance 
from the axis. 

The difference of the distances of the sight points from 
the axis of the bore, divided by the radius of the gun, meas- 
ures the tangent of the angle of elevation^ or of <f, figure I. 

The line of sight is a straight line passing through the two 
sight points. In the act of aiming it also pierces the target. 
In this case, therefore, the angle of elevation is the angle 
included between the line of sight and the axis of the bore. 

The line of departure is the line in which the projectile is 
moving when it leaves the gun. It is therefore the tangent 
to the trajectory at the muzzle. Owing to the incipient 
recoil, due to the conservatism of the system (Chapters VII, 



XX. — EXTERIOR BALLISTICS. 



XXI), and to necessary looseness of the joints between the 
trunnions and the carriage, and between the carriage and the 
wheels, the piece tends to revolve slightly about some point 
in rear, so that the projectile does not always leave the piece 
in the original direction of the axis. The angle included 
between the axis and the line of departure is called the angle 
oi ju7np,j\ figure 1. If to attain a given target the jump, 
which is almost always positive, were neglected, we would 
find d'> q and the computed value of e would be too great, 
so that the target would be overshot. 

The angle made by the line of departure with the horizon- 
tal plane is called the angle of departure, d, figure 1. It is 
with this angle that we have principally to deal in ballistics, 
as it is the angle at which the projectile actually begins its 
flight. 

The angle of projection is the angle included between the 
line of departure and the line of sight ; it may be thought of 
as the angle of elevation corrected for jump. 

The quadrant angle is the angle made by the axis of the 
bore and the horizontal. It is measured by the gunner's 
quadrant, a form of spirit level, applied to the face of the 
muzzle or to some cylindrical surface of the gun. Owing to 
the grooves in rifled guns this is preferably an exterior surface. 
See q, figure 1. 

The quadrant angle may be measured either above or 
below the horizontal plane. The term depressed or plunging 
fire refers to a negative quadrant angle. 

The angle of sight is the angle included between the line 
of sight and the horizontal plane, or s^ figure 1.* 

* This depends solely upon the altitude of the target in the astronomi- 
cal sense. It is unfortunate that the term above named should be used 
to designate this angle, as it has nothing whatever to do with the sights. 

It would be more consistent if the terms angle of sights and of elevation 
were exchanged. In the P>ench service the angle of sight is called the 
angle of site. 



XX. — EXTERIOR BALLISTICS. 



It is seen from the figure and by definition that 

Of these quantities, s is given by the act of pointing, and 
e must be computed by the methods hereafter explained. 
The above equation is principally useful for verifying the 
elevation given by the sights or for guns which are not pro- 
vided with sights. 

To determine the Jump, 

Place in front of the gun and at a distance just beyond 
the reach of the blast a slight screen. Mark upon the screen 
the point o^ at which it is pierced by the axis of the bore 
prolonged. In breech-loaders this may be done by means 
of perforated discs fitting the bore, and in muzzle-loaders 
by making ^ = and laying off on the screen the coordi- 
nates of the sight points negatively taken. 

Fire the piece and determine V. 

If then X and y are the horizontal and vertical coordi- 
nates of the center of the shot hole when referred to ^, and 
d the distance of the screen from the muzzle we have 
approximately, from figure 2, 



tan J — 



._y -Vab 



d 



^t^ d 

but ad= ^ and t= ~ neartyj 

hence tan /= | + ^^. 

If the shot strikes below the point, then y is measured 
negatively. 

X 

The lateral jump is evidently tan~^ = —, 

" Cti 



XX. — EXTERIOR BALLISTICS. 



A number of such determinations should be made since 
the method is obviously inaccurate. 

A better plan is to eliminate the effect of the perturba- 
tions near the muzzle by computing e and determining by 
experiment the value of p for an extended range of, say 
600 yards, — then j — p — e 

The jump is usually about 30' which value will be taken 
in problems in which it is required to be assumed. 

The planes of sight and of departure are vertical planes 
containing the corresponding lines. 

The computed range is the distance from the gun to the 
(second) intersection of the trajectory by the line of sight. 
The term range is also applied according to circumstances 
to the distance of the target from the gun, and to the hori- 
zontal distance to the point of impact — in case the target 
be missed and the projectile strikes some horizontal surface 
in front or rear of the target — such as water. 

Practically the dimensions of the gun may be neglected 
so that the front sight point may be considered in the axis 
of the bore and the range to be measured from either sight 
indifferently. 

In the following discussions we will also assume that the 
planes of sight and of departure coincide in the vertical 
plane containing the axis of the piece, which is called the 
plane of fire^ and that the projectile travels in the plane 
of departure. 

This is not actually true, however, for the projectile tends 
to move sideways out of the plane of departure as shown by 
the horizontal projection of figure 1. This motion, called 
the drifts is due to the combined effect of the rotation of the 
projectile and the resistance of the air ; combined with other 
causes of inaccuracy it leads at the target to lateral deviation^ 
which is meaured by the distance of the point of impact from 
the plane of sight. See Chapter XXX. 



XX. EXTERIOR BALLISTICS. 



The deviation in ran^e is similarly measured. 

Classification of Fire, 

In this classification the sights are disregarded and the 
line of fire is the straight line from the muzzle of the piece 
to the point aimed at. Similarly for general discussions the 
quadrant angle is sometimes called the angle of fire. 

Figure 3 illustrates the classification with reference to 
the vertical plane containing the target, which represents a 
certain face of a work. 

Figure 4 illustrates the classification with reference to 
the horizontal plane. The limit for direct fire is imposed 
by the principle of the rigidity of the trajectory to be here- 
after explained. 

The classification is also applied, as indicated, to the 
angles of descent. This is more accurate since it relates to 
the effect produced rather than to the intention of produc- 
ing a given effect. 



In figure 1 it is assumed without sensible error, that the lines of 
sight, departure, etc., intersect at the muzzle, and the drift is very much 
exaggerated. 



XX. — EXTERIOR BALLISTICS. 



Exterior ballistics is usually divided into tw© parts. 1st, 
in vacuo; 2d, in the air. 

I TRAJECTORY IN VACUO. 

Utility. 

The first of these is sufficiently treated in the course of 
Mechanics. Its practical utility is confined to two cases. 

1st. That of projectiles of high sectional density moving 
with comparatively low velocity as in mortars, since in such 
cases the loss of energy due to the resistance of the air may 
be neglected where only approximate results are required. 
Chapter XVI, page 1. 

2d. Cases involving the flight of projectiles in the air, in 
which some of the data are lacking, or in which the velocity 
of the projectile in one of its component directions is so 
low that the consequent retardation may be neglected. 

» USEFUL FORMULAE. 

The principal equations of this kind which are used in 
this course may be derived from equation (167), Michie, 
in which we write, as is customary, y for z, 

^ = Vsme-st; (1) 



whence 



j= Vt sin d- ^r^ (2) 



and by placing -^ =0 



(3) 



for the time to the vertex of the trajectory. 



XX. — EXTERIOR BALLISTICS. 



From the symmetry of the trajectory in vacuo, T, the 
whole time of flight is equal to 2/ or 

and 

Eliminating V by substituting this value in Equation (2), 

y^q.(T-i) (6) 

T s: T^ 

If in this we replace /by — we have F= ^—5 — (7) 

in which jj' now becomes F, the ordinate of the vertex. 

That is, the height of the vertex in feet is nearly four 
times the square of the time of flight in seconds. 

Equations (6) and (7) are important, and should be re- 
membered, as they are frequently used in approximate solu- 
tions in the air. 

If in Equation (169), Michie, rewritten according to the 
usual nomenclature, or 

y = X tan — -r--- ^-^ (8) 

in which ^is the height through which the projectile must 
fall to acquire the velocity F, we make j = 6 wq may 
determine the range X 

2 V sin cos (9 _ V sin 2 d 

X =: (y) 

g g 

Therefore the range will vary less from variations in 0, as 
d approaches 45°. 
Also, for the same value of B, as in S. B. mortars, 
X: X' -.'.V^: V'\ 



XX.— EXTERIOR BALLISTICS. 



But, considering the powder as a reservoir of potential 
energy, frona the equation of energy we have approximately 

And assijming the weight of the projectile, JV, to be con- 
stant for the same piece 

w: w'v.E'. E'wV^ \ V'^::X: X\ 

Therefore, in a S. B. mortar the charges are proportional 
to the ranges. This is of importance in regulating charges 
and works well in practice. 

If in equation (9) we substitute the value of F in equa- 
tion (5), we find, if we call g=32 approximately and ^=45°, 
X=16 T' or 

T= ^ (10) 

which gives a rule for timing mortar fuzes. 

RESISTANCE OF THE AIR. 

To give an idea of the pressure exerted on projectiles in 
the air and consequently of the insufficiency of the preced- 
ing formulae for practical use, except in the cases cited; it 
will suffice to say that a velocity of the wind of about 100 
miles an hour is designated in the Ordnance Manual as a 
"hurricane that tears up trees, carries buildings before 
it, etc." 

In projectiles moving with the high velocities now attained 
the pressure is over 80 times as great as that assigned to 
the hurricane. 

EXPERIMENTS TO DETERMINE THE RESISTANCE OF THE AIR. 

Experiments have been constantly made since Robins, 
called the " Father of Gunnery," began to investigate this 
subject about the middle of the last century. But these 



:XX. EXTERIOR BALLISTICS. 



gave untrustworthy results owing to the lack of suitable 
velocimeters. 

It is upon the investigations of the Reverend Francis 
Bashforth, conducted under the auspices of the British 
Government from 1865 to 1880, that our knowledge of the 
effects of this resistance is based. 

RESULTS OF EXPERIMENTS. 

Resistance. 

Bashforth's experiments demonstrate that the resistance 
varies with the quantities shown on the following tabular 
scheme. 

'1. Area of cross-section or ^^, Chap. XVI. 

2. Density of air. 

3. k, Chap. XVI,|l. Meridian section]^ ^^^^^^^» 



Resist- 
ance 

varies 

with ^ page 2, viz.: |jj Velocity of projectile'. 

1. That the resistance varies with the area is recognized by 
all experimenters. 

2. The effect of variations in the density of the air, whether 
due to variations in barometric pressure, in temperature or in 
humidity, or from the passage of the projectile through strata 
of varying density, is allowed for m refined computations by 
suitable coefficients. For this treatise the effects of such 
variations are neglected. 

3. Variations in k due to slight variations in the meridian 
section are also neglected, although they may be similarly 
corrected, see b below. 

1. As to the Meridiafi Section^ viz, : 
(a) Form of Head. — Bashforth in his experiments used 
projectiles of the same calibre and weight, and having heads 
of five different shapes. These were, 1st, hemispherical; 
2d, hemispheroidal, with axes in the ratio of 1 to 2; 
3d, ogival, radius of head 1 diameter; 4th, ogival, radius of 
bead 2 diameters; 5th, fiat. 



10 XX. — EXTERIOR BALLISTICS. 

The resistance was greatest on the flat-headed projectile, 
and least on the hemispheroidal and ogival of two diameters. 
Rashforth concludes that the resistance offered by the air to 
the motion of elongated projectiles is but little affected by 
the more or less pointed apex, but depends chiefly upon 
the form of the head, near its junction with the cylindrical 
body of the shot. At this point the forms of the hemisphe- 
roidal head, and of the ogival head of two diameters radius, 
are about the same, and their resistances are nearly equal. 

(/^) Form of Body. — Recent experiments by Krupp have 
shown that the resistance varies also with the shapes of the 
sides and rear of the projectile, and with the character of its 
surface. 



2. Retardation and Velocity, 

Rashforth's method was one of interpolation founded on 
the use of velocimeters of Class II, by which he determined 
by means of finite differences the retardation of the pro- 
jectile at certain points of its trajectory at which the velocity 
was known. 

Everything else being constant, the relation between the 
retardation and the velocity was known for each of the veloc- 
ities observed at any one fire. And by varying these veloc- 
ities as by varying the initial velocity or the distance of the 
gun from the targets, an indefinite number of velocities could 
be observed and their corresponding retardations computed. 

Finally, the law connecting the velocity and the retardation 
could be deduced by analysis, or expressed by plotting a 
curve of which the retardation and velocities are the coordi- 
nate axes. 

For the same velocity the retardation was found to vary 
with (') the sectional density of the projectile, its f ) meridian 
section and (') surface, and with the (*) density of the air as 



XX. — EXTERIOR BALLISTICS. 11 

affected by its temperature, barometric pressure and its 
humidity. 

Accordingly, such a law must for convenience be reduced 
to standard conditions, that is, when (i) W (in pounds) = d^ 
(in inches), i. e., when we have the unit projectile^ and when 
the (2) proportions and (3) surface of the projectile are well 
defined, and the (^) density of the air is at a known standard. 

Variations in these four conditions are subsequently 
allowed for by suitable empirical coefficients of which we 
shall deal with only that relating to the sectional density. 

It may be stated however that Bashforth used a M. L. R. 
gun firing studded projectiles^ the points having a radius of 
IJ calibres. The more recent B. L. projectiles, having 
sharper points and smoother surfaces, reduce the retardation 
by 5 or .10 per cent. See page 10. 

bashforth's method. 

, He placed 10 targets at a constant interval of 150 feet=/. 
This gave such a number of observations at each fire that 
they served to correct each other by the principle of con- 
tinuity, so that the final order of differences would be either 
0, or would change very slowly. Examples of this are seen 
in the methods used in correcting tables of squares, cubes 
and of logarithms. 

For this purpose the advantages of instruments of Class 
II. over those of Class I. are obvious. Such instruments 
ordinarily give only the velocity at some point between each 
pair of targets. But Bashforth sought the velocity at the 
target itself as follows : 

Calling (7;,,) the velocity at the target which is at a distance 
X from the gun 



12 XX. — EXTERIOR BALLISTICS. 

In measuring velocity it is customary to express j as a 
function of t, in which t (one second) is the constant. 
But when, as in these experiments, / is constant, it is 
advisable to express the velocity by varying the value of/. 
Consequently, calling r^ the retardation at the distance x 
and observing that, since this is a negative acceleration, we 
may neglect the minus sign resulting from differentiation, 
we have "^ 



~di~~dF 



^{ij=i^^^ (12) 



The object of presenting the retardation in this form was 
to make it an explicit function of the cube of the velocity 
since Bashforth had reason to believe that the retardation 
followed what is known as the cubic law.^ 

In order to apply equations (U) and (12) practically, it 
is necessary to find by experiment such finite values for dt 
and d'^t that, when substituted in the preceding equations 
they will give proper values for v^ and r,. Or, calling these 
finite values A/, ^nd AV, 

^^=^ (11') 

'■.= ~/r^l (13') 



* The simplicity of such a law has always proved attractive to in- 
vestigators of thir, subject. Sir Isaac Newton took it to vary with the 
square of the velocity, and others with varying powers of the velocity 
corresponding to certain limiting velocities. 

Newton's law has recently been proved nearly true for the high veloci- 
ties and smooth pointed projectiles now employed. It will be seen here- 
after how Bashforth corrected the cubic law by an empirical coefficient 
corresponding to the velocity. 



XX. — EXTERIOR BALLISTICS. 13 



DETERMINATION OF VELOCITY AND RESISTANCE. 

Referring to Bashforth's experiments, let s denote the 
distance from any origin to the first target. Then j + / 
will be the distance from the same origin to the second 
target and s-\-(n — 1) / the distance to the «'* target at the 
distance x, and so on. 

Also, let 4 denote the time from any origin until the 
first target is reached. Then fs+(n-i)i will be the time from 
the same origin until the n^'^ target is reached and so on. 

Now, let ^1, 4> 4> etc., denote the 1st, 2d, 3d orders of 
difference and d\ d'\ d"\ the successive terms in these 
orders of difference so that 4'" will mean the third term 
in the second order of difference and so on. 

Then 4+i~4=^/> which will be the time of passage of 
the projectile between the 1st and 2d targets and 

4+21 4+1 = ^1 y 

and d-l*—d^=d^ and so on. 

We may therefore form the following table which may 
be filled up from experiment as shown below numerically, 
and graphically by the diagram, figure 5. 

The dotted lines in the diagram serve to indicate the 
successive orders of difference after the manner of the 
brackets in the table. 

TABLE. 

No. of -p.. . Time of Orders of difference. 

target. distance. ^^^^^^^ ^^ ^^ d^ . , , d^n-i) 



1. 


s 


^8 


2. 


s + l 


4-fi 


3. 


j + 2/ 


4+21 


4. 


5 + 3/ 


4+31 


5. 


j + 4/ 


4+41 



[ dJ' etc. 



\d. 









14 :XX. — EXTERIOR BALLISTICS. 





NUMERICAL EXAMPLE. 










times. 


^1 


^. 


^8 


1. 


S 


3.0526 


.1090 






2. 


j+150 


3.1616 


.1114 


.0024 





3. 


J + 300 


3.2730 


.1138 


.0024 


1 


4. 


J + 450 


3.3868 


.1163 


.0025 





6. 


^ + 600 


3.5031 


.1188 


.0025 





6. .y + 750 3.6219 

From the algebra we have 

^.+.=4+H' + « ^^/ + «^"~;y3~^^4' + etc. 

Arranging the terms of the second member with refer- 
ence to n which is arbitrary, we have 

4+ni=4 + « W-i 4' + J 4'-etc.) 

+ ^(4'-4' + etc.) (13) 

Now /g^nb being a function of the space (s + nl)^ may be 
developed by Taylor's formula. Hence we have 

/s+ni=/(^ + «/) =^«+ ^«^+ -^T2- + ^'"- 
or since, ds=lf 



2 



Equating the coefficients of the first power of n in the 
second members of the two identical equations (13) and 
(14), we have 

<^/s=<^i'-J4'+^^3'~etc.=A4 (15) 



:XX. — EXTERIOR BALLISTICS. 15 

which is the finite value of dt^ for the constant increment 
of 5. 

In other words, and as shown by figure 5, if Bashforth 
had taken d-l to be the increment of time at the first tar- 
get corresponding to ds^ the velocity computed would have 
been the mean velocity between the 1st and 2d targets and 
would have been too small. Consequently this increment 
is diminished by \ d^ . This makes the velocity too great, 
so that \ d^ is added, the approximation increasing with. 
the number of targets employed; since, under the same 
circumstances, the greater the number of observations, the 
more truly can the law be determined; or, mathematically 
speaking, the greater will be the ± correction applied to 
d^ since the greater will be the number of orders of 
difference. 

Therefore, for the target at the distance s or the first 
target, 

_ 2__ 150 ""^^ 

Similarly for the «'* target at the distance x = s-\- (n — 1)/ 

150 / ..„ 

""- - d^ - i 4° + ^4" - etc.- df, ^ (_,,, ^^^^ 

The number of the targets at which velocities could be 
obtained is determined by the number of targets employed 
and by the number of orders of difference which the law of 
retardation permits. If n' be this number, then velocities 
may be determined at (n — ;/) points. 

Similarly, we have the coefficients of the second power 

d% = d/—dj + etc. = A V„ (18) 

and for the «** target 



rx = 



-^ AV, = p^.( d^^d,^ + etc. ) (19) 



16 .XX. — EXTERIOR BALLISTICS. 



Example. 

The velocity at the 4th target in the preceding table is 
1304: and the retardation 246.5.* 

RESULTS OF THE EXPERIMENTS. 

If the cubic law had held true for all velocities, the co- 
efficient k in Equation (1), Chapter XVI, could have been 
replaced by some explicit function of i^. 

But while this was found to be nearly true for velocities 
between 1100 and ]350 feet, it failed for velocities above 
and below these limits, as Bashforth found by increasing 
his velocities progressively from 100 to 2900 feet. 

He accordingly introduced an empirical constant k* by 
which to correct the departure from the cubic law so that 

r — — /&' 7/ 

W ' 

and as k' is a very small quantity, he replaced it by 

/ir= (1000)3 >^', 
so that 

Table I gives the value of K for the velocities named 
therein and figure 6 is plotted from the indications of 
Table I. 
Example. 

A 12.5 inch shell weighing 802.25 lbs. has a velocity of 
1400. The total air pressure is 1394 lbs. and the retardation 
is 55.96 at the instant that the velocity is 1400. 

Figure 7 gives the pressure on what is called a circular 
inch (that is a circle of which ^=1 inch) on spherical pro- 
jectiles, curve A; on studded oblong projectiles of which 

*Throughout this chapter velocities will be expressed numerically, as 
the unit of velocity, or foot-second, may be understood. 



XX. — EXTERIOR BALLISTICS. 17 

the radius of curvature of the head is | d^ curve B ; and 
on modern smooth b. 1. projectiles in which the radius = 2 d, 
curve C, derived from recent experiments by Krupp. 

In curve B two remarkable inflections are observed. One 
at about 1090, the velocity of sound, and the other at about 
2413, that of air rushing into a vacuum. 

The first velocity marks the passage of the projectile into 
a medium undisturbed by the explosion of the gun or by its 
own passage. The second denotes the formation of a 
vacuum in rear of the projectile which increases the pressure 
to ajDout double that of the barometric pressure of the 
atmosphere. 

In firing at troops, particularly in sieges, it is important 
to have the terminal velocity exceed that of sound, so that 
the projectile may precede the warning sound made by its 
passage through the air. 

The irregularity of curves B and C shows the impossibility 
of expressing by any simple law the relation between 
velocity and pressure. 

i 
Final Velocity. 

Figure 7 enables us to appioximate closely to the final 
velocity of the projectile. 

This term, which must be carefully distinguished from 
the ter7ninal velocity (Chap. I), is that velocity which the 
projectile has acquired in falling when the resistance of the 
air becomes equal to the accelerating force of gravity. This 
velocity is necessarily uniform and a maximum. 

For example, a 64 lb. projectile, 6.3 inch in diameter, has 
a weight per circular inch of 1.613 lbs. If it belongs to the 
class of projectiles used by Bashforth, an equal and contrary 
air pressure will result when a velocity of nearly 900 f. s. 
has been acquired. But for more modern projectiles a 
higher final velocity will result. 



18 XX. — EXTERIOR BALLISTICS. 

This velocity which formerly had only a theoretical signifi- 
cance, is becoming important in consequence of the great 
heights and high angles of fire now used in mortar firing. 

The S. C. Mortar has thrown its shell over 3 miles into 
the air with an angle of fall of about 75°. 

The result can be reached more exactly by a method of 
approximation based upon the fact that K enters into equa- 
tion (20) in the first power while v is cubed. Consequently, 
the first trial values of K will not greatly affect the result, 
and we may finally find a velocity and corresponding value 
of K which will satisfy the eqi^-^Hon 



TRAJECTORY IN AIR. 

GENERAL SOLUTION. 

Notation. 

Let O VR = S, figure 8, represent a trajectory. 

Let V be the muzzle velocity in the line of departure. 

ds 
Let v= —j-he the velocity in the direction of the tangent 

at any point of which the coordinates are x and y. 

Let u be the horizontal component of the velocity v. 

Let 7j\ v'\ u\ 2^", be the corresponding tangential and 
horizontal velocities at the beginning and end of any arc, 
the coordinates of the extremities of which are {x*^ y), 
{x",y"). 

Let (p be the variable inclination to the horizontal of the 
tangent to the trajectory; then u^v cos (p. 

Let 6 and g9, measured as in the figure, be the particular 
values of q) for the angles of departure and of fall. 



XX. EXTERIOR BALLISTICS. 19 

Let a and /? be the values of q} at the beginning and 
end of any arc when the velocity is v' and v". 

Then the figure shows that 6 — a — ^ or the angle in- 
cluded between the tangents is the change in inclination 
due to a change in velocity from v* to v'\ 

Similarly A=^— (—<») = ^+co is the total change in 
inclination. 

Let q) (read (p " dash ") be the inclination to the hori- 
zontal of any chord of the trajectory. 

Let 2/= = = u sec cp be the component velocity of 

cos (p 

V in the direction of the chord, and, as above, let v\ v" be 

the component velocities in the direction of the chord at 

the beginning and end of the arc (^',^')j (^"> ^")- 

Let /,' /" be the times measured from any origin to the 

instants when the velocities are respectively 

( z/', z/"), P", v^), etc. 

Note that /">/', v''<v'. 

Let t—t"—t' for any arc and r=time to vertex, T\-\- 
time from the vertex to R^ T^ be the whole time of flight, or 

Similarly, 

Let Jf', y, be the computed coordinates of the vertex 
measured from 0\ and X^, K^, the computed coordinates 
of the same point measured from ^, so that the computed 
range, X=0 R=X' -^-X^. 

The figure shows that the notation of z;', «', cp^ changes 
from the ascending to the descending branch to z'^, u^^ cp. 
This distinction will be observed throughout when the 
branches are separately considered; but, when the trajec- 
tory is considered as a whole, v\ z;", «&c., refer to the 
beginning and ending of any arc. 



20 XX. — EXTERIOR BALLISTICS. 

Let the ordinate at D represent the height of a target at 
the distance OD. Then DR is the dangerous space for 
that target. If we aim at the center of the target this 
evidently measures nearly twice the ± error permissible 
in estimating the distance, as a measure preliminary to 
determining the value of d required to strike the target at 
some point of its height. See Chap. I., p. 3. 

The dangerous space is known herein as D. S, 

Eesolution of Motion. 

Let AIR, figure 9, be some arc of the trajectory to 
which //is the tangent at /, p is the radius of curvature, 
g the acceleration due to gravity, r the retardation due to 
the resistance of the air. 

Then from the figure, for the horizontal retardation, 

-— - = r cos (p (21) 

and, from Mechanics, for the normal component of the 
deviating force of gravity ,^^ 

(32) 





-=gcos cp 


, 1 dcp . dt 

but - = -/- X -77 

p ds dt 


= — ^ and. therefore, 
dt.v 




dcp 



(23) 

Dividing Equation (23) by (21) member by member, we 
have, after transposing, 

dq>= 1^ (24) 



XX. — 'EXTERIOR BALLISTICS. 



21 



Integrating between the limits (p=^a and ^=/5 and the 
corresponding values of u^ we have 



/3 y nf' 



or 



A ^g 




du 
rv' 



From equation (21) we have by similar means, 




du 



r cos q) 



or 




du 



cos q) 



Similarly, from the relations between x,y, t, and Uy 




u dt^=- 




u du 
r cos q) 



or 




u du 
rcos (p 

u du 



or 



r cos cp 



u du 
r cos cp 



tan ^, 



tan ^. 



(25) 
(25') 

(36) 
(26') 

(27) 

(27') 
(28) 

(28') 



22 XX. — EXTERIOR BALLISTICS. 

If these general equations (25-28) could be integrated, 
they would give the change in the coordinates of an arc of 
the trajector}'- (x^'—x^), (7"— j^') corresponding to a change 
of horizontal velocity {u^—u")^ the time t required to 
make this change, and the change of inclination d, corre- 
sponding to the same change in the velocity. 

But the second members contain three variables, u, cp^ 
and r, not connected by any law, and hence the integration 
is impossible. 

Bashforth's experiments, however, give the law connect- 
ing u and r, and in order to avoid the difficulty arising 
from the presence of the variable cp we assume for it a 
constant mean value qy. That is, that on the same princi- 
ple as that by which we have neglected the small vertical 
component of the resistance, we now neglect the small 
component velocity in a direction at right angles to the 
chord, and suppose the length of the arc to be that of the 
chord, although its curvature is retained. 

COROLLARIES. 

I. Equation (23) may be written 
d(p __g cos (p 
~dt V ' 



whence, by dividing member by member by 
cos ^, w 
dqp __g 



dx 

-—=zv COS cpf we obtain 



sul 
dcp _W 



Calling esc- -^ — and substituting we have 



dx 'Ze 



(30) 



XX. — EXTERIOR BALLISTICS. 23 

Equations (29) and (30) express the rate of change of the 
direction of the tangent to the trajectory, or the rate at 
which the trajectory is becoming curved, as a function of 
the range. Equation (29) ilhistrates the remarks, Chap. I, 
top page 3, and Equation (30) explains the importance of 
Chap. XVI, p. 1. These equations set forth a most import- 
ant property of the trajectory in air. 

Figure 10, >vhich is carefully drawn to a scale, represents 
in curve A the trajectory in vacuo of a projectile fired with 
e = 30° and V = about 1700 f. s. 

Curves B and C represent the trajectories m air of spher- 
ical projectiles as follows : 

B. 15 inch ; W= 450 lbs. d = 14.87 inch. \V= 1700 

C. 24 pdr. ; W = 26.92 lbs. d = 5.9 inch. 5 (9 = 30° 
Since from Chap. XVI, p. 2, the elements of a trajectory 

;When 6 and V are given depend on the ballistic coefficient 

■— r, It appears that the 24 pdr. projectile would describe 

the trajectory B if its weight were increased to 70.86 lbs., 
the calibre remaining constant; or, by reducing the calibra 
to 3.637 inches, the weight of the projectile remaining con- 
stant. The objections to this are given Chap. XVI, p. 4. 

II. If in equation (29) we substitute for 2^ its value 
\p g cos (pf we find 

dg) 1 J dx 

-~ = or d o) cos (Z) = — 

dx p cos (p ^ ^ p 

Integrating this equation between the limits -(- 6 and — w, 
figure 8, corresponding to O and X, and assuming some mean 
value of p = p' by which to measure the flatness of the tra- 
jectory, we have as a measure of its mean curvature, 

1 _ sin + sin 6> 

7" - X ^^^^ 



24 XX. — EXTERIOR BALLISTICS. 

Although from equation (22) and from experience it is 
evident that, owing to the variable value of g cos cp^ with 
the sight set for a certain range it is impossible to hit any 
desired point of a vertical circle described about the gun 
with the range as a radius; yet, as shown by equation (31) 
and figure 11, if the altitude of the target or the angle of 
sight s, be small, the decrease of g>' tends to compensate 
for the increase of 6', so that sin 6' + sin w' may not differ 
greatly from sin 6 -\- sin w : OX' = OX cos s will also be very 
nearly equal to X, Under these circumstances the two values 
of p' will not differ greatly from each other. 

Under this assumption we may consider the mean curva- 
ture of the trajectory to be constant or the trajectory to be 
practically rigid, so that for small altitudes the elements of 
the trajectory measured along the chord may be safely 
assumed to be independent of the inclination of the chord 
to the horizon. 

Equation (30) shows that this assumption will increase 
in truth when the sectional density and the muzzle velocity 
increase, which is the present tendency. The principle 
involved is of especial importance in the rapid fire of 
modern small arms and field pieces, since it permits the use 
for inclined ranges of sights graduated for horizontal ranges, 
when the ± angle of sight is less than about 10°. 

In such cases the change, s' figure 11, in the angle of 
departure, may for a first approximation be safely taken to 
be equal to s, and this change is automatically made by the 
act of pointing. 

Actually however, when s is positive, p' decreases and 
conversely; so that in firing up hill the projectiles tend to 
fall short and in firing down hill they tend to pass over the 
object. 



XX. EXTERIOR BALLISTICS. 



NIVEN'S METHOD. 

Various expressions have been deduced for the value of ; 
that of Mr. W. D. Niven, F.R.S., obtained from an expand- 
ing series, is one of the most simple and, for illustration, a 
particular value of 0, deduced for equation (25), is herein 
applied to all cases indifferendy. 

The appendix to this chapter contains the means of arriv- 
ing at more exact values of cp. 

Under this hypothesis we shall adopt, as a sufficient approxi- 
mation for small angles of 8 less than about 3°, 

= ^, (32) 

and for larger angles the approximation 

— tan a -\- tan 6 ^,«„x 

tan = J- -. *(33) 

From the notation we have 

u = V cos ; du =^ dv cos ; v' = u' sec 0, etc. 
Substituting these values in equation (25), and replacing 
r by its new value -^ -^r[TK()()] ' ^^ ^^^^ 



S = cos (pg 




* These values of (p give good practical results. 



26 XX. — EXTERIOR BALLISTICS. 

In this equation ^ is expressed in circular measure, that is, 
in terms of the ratio tt = 180°. To reduce it to the corre- 
sponding number of degrees, d, we have, 

Ttd 
d:7c::d:180 or ^ = -^^. 

loO 

Substituting this value of S in the above equation, and 
representing as hereafter the ballistic coefficient ^ by C, we 
have, after reduction, 



^ , cos 180^ (1000) 

Ca = 



7t 






In this ^ is a function of v, and therefore changes between 
the limits of integration. Means have, however, been found 
for determining its mean value for limiting velocities. 

The value so determined is nearly its arithmetical mean. 
Therefore we have, calling this mean value K\ 

^^^cos0i8^o_oo): r-s^ 

Similarly, we have 

And representing by s the length of the chord, the co-ordi- 
nates of the extremities of which are {x' x") (/ y") 

csj^' ry} (36) 






We have also 



X 



II 



s cos andji/ = y" — / = s sin (p 



XX. EXTERIOR BALLISTICS. 27 



These equations are in a form to be integrated, and Tables 
II, III, IV have been computed for a projectile in which 
^ = 1, as follows : 

Assume any velocity v^ sufficiently low as the origin of in- 
tegrals, and assigning proper values for K', integrate equa- 
tions (34, 35, 36) between v^ and successive values of v'. 
We thus obtain what are called angular /unctions dy> , time 
functions^ r^> , and space functions, (Ti/ , which may be ex- 
plained by reference to the time functions in Table II. 



Explanation of the Tables. 

Considering the acceleration to be positive. Table II may 
be considered to express by its functions the several times 
r, r', r", etc., required to give to a unit projectile, starting as 
from rest, the several corresponding velocities under the ac- 
tion of a variable force equal to the variable resistance of the 
air. 

Table III may be similarly understood to express the space 
in feet <t, a', a", etc., over which such a force would have to 
act in order to increase the velocity from some initial velocity 
as 0, to the several corresponding velocities given. 

It is evident that each function in each table might be 
numerically diminished by the first function in its own table 
without affecting the value of the table or the velocities to 
which it applies, since it is only the differences between func- 
tions that are considered. 

Conversely, considering the acceleration as negative, if any 
time function as r', figure 12, measured from any origin /^ , 
corresponds to a change v' — v^ in the velocity measured 
from any origin v^ , and r" similarly corresponds to a change 
r" — v^ , then r" — r' can correspond only to the particular 
change &' — v". So that knowing r" — r' ^=^t, and either 
z/ or v", we may determine the other velocity; and con- 



28 XX.' — EXTERIOR BALLISTICS. 

versely as to /, r', or r", without regard to whether the 
difference is positive or negative. 

Similarly for the angular functions. If any angular func- 
tion d', figure 13, corresponds to a change v' — v^, and d" 
to a change jy" — v^ , then 6* — d" = ^ will correspond to a 
change v' — v". 

In all cases we have two pairs of unknown quantities, of 
which the difference between one pair and one of the other 
quantities is needed to determine the remaining quantity. 

These data are given by the conditions of the problem, or 
are suppHed by certain assumptions to be hereafter explained. 

Example from Table II. 

The change of time (or time required) for a change of 
velocity of 300 when the greater velocity is 1400 is 231.9883 
— 230.5314 = 1.4569 sec. When the lesser velocity is 1400 
it is 0.8697. 

If in the first case the time from some given origin, say the 
firing of the piece, until the velocity was reduced to 1400 was, 
say, 2 seconds, then the time measured from the same origin 
until the velocity fell to 1100, would be 3.4569 sec, and so on. 

PRACTICAL FORMULAE. 

For the ascending branch Equations (34), (35), (36) may be 
written.* 

Cd — cos (p{di> — 6-^") ; (I) 

a = r-> — T^n ; (II) 

Cs = a^> — <T~v". (Ill) 

Whence from III, 

Cx = Cs cos = cos 0(cr^/ — (Tin); (HI') 

Q/ = Cs sin = sin 0(cr;,/ — (T^"), (HI") 

* Similar equations serve for the descending branch. 



XX. EXTERIOR BALLISTICS. S9 



The Greek letters in the second members of the above 
equations are the corresponding tabular functions found 
respectively in Tables IV, II, III. 

These tables are arranged like logarithmic tables. Except 
■where small changes of the functions are considered, for sec- 
tion-room work the column of differences need not ordinarily 
be employed, the nearest function or velocity being taken. 

It is evident that the nearer the chord is to the arc, the less 
will be the difference v — v, and the more accurate will be 
the result. In practice, it is considered sufficiently accurate 
to divide the trajectory into two arcs, at the vertex. 

For simplicity, and by the principle of the rigidity of the 
trajectory, unless otherwise stated, the chord is taken hori- 
zontal. 

It is important to note that although ranges are generally 
given in yards, the chords of trajectories (Chapter I) are ex- 
pressed in FEET. Neglect of this frequently leads to failure in 
practical work. 

Example. 

To illustrate the use of the tables in calculating the elements 
of a trajectory, we will take the 100-ton Armstrong gun and 
consider figures 8' and 14. 

Data. 

V= 1833; d = ll°50'=ll°.83i; PF=2005 lbs.; ^*=17 in.; 

hence 

C= 0.14414, log-^ = T. 15879, co-log -^ = 10.84121. 

This quantity must always be determined before any other 
work is attempted. 



*The d above must be distinguished from the angle d elsewhere 
discussed, 



30 XX. — EXTERIOR BALLISTICS. 



Elements required. 

1. The remaining energy at any point or : e, 

2. Height of trajectory at any point ot y. 

3. Total range or X. 

4. Angle of fall at end of range or qd. 

5. The dangerous space, D. S. , for any range. 

6. Time of flight to any distance or /. 

7. Tinxe of flight for the whole range or T. 

8. Inclination of the trajectory at any distance or <p. 

9. Having the initial velocity to find the value of B to at- 
tain a desired range. 

etc. etc. etc. 

1st. To find the remaining energy, we find the remaining 
velocity as follows : 

From figure 8 the change of from the origin to the 
vertex is ^ = « = d. At this point /? = ; therefore, from 
equation (33), 



- tan Of 4- tan tan 11° 50' 

tan <2!> = — ' — 



2 2 

= tan 5° 58' 50" = tan 5° 58'. 83. 

As we shall have to use the logarithmic functions of 0, we 
now tabulate them as follows ; 

logs. co-logs, 

sin T. 01783 10.98317 

cos 1.99763 10.00237 = log sec 0. 

To find v' we project V on the horizontal or determine 
«' = Fcos B\ thence v' = «' sec 0, or «' = 1794, v' = 1803.9. 



XX. — EXTERIOR BALLISTICS. 31 

Now to find v'' we transpose equation (I) to read 

COS 

in which 

Oj,' = 1803.9 • 

In Table IV we find 

di803 = 84°.8199 
p. p. for 0.9 = 21 



84°. 8220 



Consequently, all the quantities in the second member 
being known, we may write 

14414 
6-r= 84°.8220 - ll°.83i ^--l-**-^* 



log'-i 1.99763 
= 84°.8220 - 1°.7149 = 83°.1071. 

From Table IV, again, we have for the velocity correspond- 
ing to d = 83°.1071, v" = 1318 for the remaining velocity 
at the vertex, and hence 



«" = 1318 cos = 1310.8. 

The origin is now transferred to the vertex, and we treat 
the descending branch similarly to the ascending branch. 

The angle a for this arc is evidently 0, and u^ = u" just 

found, but the value of /? = g? required to find is unknown. 

It is therefore necessary to assume a value for it. Equation 

(29) shows that it will be greater than ^, and experience 

4^ 
proves that it is nearly — or a? = 15°. 77, 



3S XX. — EXTERIOR BALLISTICS. 

If we assume an incorrect value, as will generally be the 
case, the error is corrected by a subsequent operation. So 
let us assume an incorrect value, or co= 16°, as a first ap- 
proximation. Thence 

tan 16° oo n/ K 

tan (p = — - — = tan 8 9'. 5 
— 4 

I 
and 

v^ = 1310.8 X sec 8° 9'.5 = 1324.1 and (J- == 83°.1406. 
Using equation (I) again, we have 



*,„ = sr.im - ^-5^-5 16° 

= 83°.1406 - 2°.3298 = 80°.8108; 



and v^^ = 1061, u^^ = 1050, and v^^ , the velocity along the 
tangent, := u„ sec. w = 1093. The vertical component of v 
will be = «yy tan w = 301. 

The component energies are generally useful for doing work 
against targets which are nearly vertical, as the walls of vessels 
or forts ; or horizontal, as the decks of vessels or the roofs of 
magazines or casemates. We therefore find that while the 
projectile started with energy in the direction of the tangent 
or ^y = 46,700 foot-tons, it now has ^e/,, = 16,604 foot- 
tons ; only about one third as much as when it started. 

Its component horizontal and vertical energies are 15,320 
foot-tons and 1260 foot-tons, respectively. 

The steps of the problem can be clearly followed in the first 
stages of Example I, which is given in the form used for 
written recitation. 



XX. — EXTERIOR BALLISTICS. 



S3 



la. 



Data: F=1833; ^ = 11° 50' ; W=2005; ^=17 in. 
Required U^,^^. 



Statement of Steps. 


Terms. 


Quantities. 


Functions. 


Logs. 


I- C = ^=0.14414 


c 

T 


17^ 
2005 

O.14414 




2 . 46090 
3 -30211 




1.15879 




c 






IO.8412I 


- tan 9 
2. tan0= 










= tan 5° 58'. 83 


tan B 


tan 11° 50' 
2 




9.32122 
.30103 




tan 


tan 5° 58'.83 




9.02019 




cos 

I 


cos 

sec " 




9-99763 




cos 


10.00237 




sin 

I 

sin 

cos 6 


sin 




9.01782 




I ,, 
sin 




10.98317 


3. u'= F'cos = 1794 


cos II 50 

1794 




3-26316 
9.99067 




3-25383 


4. v' = u' sec (p = 1803.9 


sec 

v 


1803.9 




10.00237 




3-25620 


^■'-^■-'-"-co%-'^^' 


h' 


5l803.9 


84.8220 






C 

d 


n^83i 




1. 15879 
1.07300 




sec 






10.00237 






I3I8 


I. 7146 


0.23416 




83.1074 





34 



XX. EXTERIOR BALLISTICS. 



Statement of Steps. 


Terms. 


Quantities. 


Functions. Logs. 


6. u' =: «^ = v" COS 

= I3IO.8 


COS 


1318 
1310.8 


1 3-II992 
9.99763 

3.I1755 


7.tan^='^"/ = 8"9'.5 


tan /? 

tan 
cos 
sec 
sin 
I ~~ 


tan 16° 

tan 8° 9'. 5 
cos " 
sec '* 
sin '* 
I ., 
sin 




9-45750 
.30103 

9.15647 

9-99558 

10.00442 

9.15201 




sin 


10.84799 


8. vi = u sec = 1324. 1 


sec 


1310.8 
1324-2 




3-11755 
10.00442 




3.12197 


9. d- = (5- — CJ sec 

= 1061 


d 
sec 


^1324. a 

16" 

I06I 


83.1411 
2.3298 


1. 15879 

I. 20412 

10.00442 


The determination of g is 
omitted. 


0.36733 


80.8113 





XX. EXTERIOR BALLISTICS. 



35 



lb. 



Data as in la. 

Required » at 1000 yards = 3000 feet. 



Statement of Steps. 


Terms. 


Quantities. 


Functions. 


Logs. 


J. Determine whether to 
use or by finding 
whether 3000 is < or > 
X' .: 


cos 

I 
C 

X' 


O"i803-9 
15045 


44456.3 
42275.8 


9.99763 


jr'=cos0(a--,-o--„)X^ 
= 15045 ft. =;= 5015 yds. 

.*. use 


2180.5 


3.33856 

IO.84121 

4.17740 


2. 0--,, = (T-, — Cx sec (p 
v" = 1697 


sec 


3000 

1697 


44456.3 
434-8 


I. 15879 
3.47712 

10.00237 
2.63828 




44021.5 





36 



XX. — EXTERIOR BALLISTICS. 



Data as in la. 

Required V from data of ascending branch. 



Statement of Steps. 


Terms. 


Quantities. 


Functions. 


Logs. 


y:=Y' 










= sin 0(o--,-o--„)i 


sin 






9.01782 


^1576.1 feet. 


^i' 


Cri803.9 


44456.3 






^-." 


cri3i8 


42275-8 
2180.5 


3-33856 




C 






IO.84121 




v 


1576. I 




3-19759 



Similarly we may find from the value of that 
r, = 1713 feet. 

The difference, 1713 - 1576.1 = 136.9 is evidently due to 
the error in our assumption of the value of gj, and therefore in 
our deduced value of ; the effect is to increase the range as 
shown by figure 14. 

This leads to the means of correcting od to be explained. 

3. To find the range. 

With the assumed value of gd and we find X^ by the 
method described in lb, or X^ = 11949 feet. 
Ave also have X' = 15045.4 '' 

Z = Z'-|-X, = 26994.4 '' 

But this range is too great by the distance B^C, figure 14. 
To find this distance we assume that this short arc coincides 
with its tangent, which by assumption makes an angle of 16° 
with the horizon, 



XX. — EXTERIOR BALLISTICS. 37 



Therefore 



B'C = -i??^ = 477.4 ft. and X, = 11471.6 ft. 
tan 16 

and X = 26517. ft. = 8839 yds. = 5 miles + . 

4. To find the incHnation at the end of the range or the 
angle of fall, oo. 

We can vouch for only the elements of the trajectory in the 
ascending branch, but if we can determine the range as by 
firing or by the method just described, we may approximate 
closely to the angle of fall. 

For 

V tan GD 
tan0 = ^ = — -; 

. •. tan G? = V and Ce9 = 15° 20' 28". 
^/ 

In the example this gives a difference of but 6. 8 feet in the 
two values of K, which difference can be further reduced to 
by successively approximating to the true value of oj, or 
G) = 15° 18' 12" ; and therefore ±^=7° 47' |i and ~v, == 
1323, z7, = 1067.3, X, = 3840 yds. 

These values will be hereafter employed, since it is most 
important to have a correct knowledge of the elements of the 
trajectory at its further end. 

Practical Methods for Detennining w. 

1. Fire through a screen near the point of fall, and note the 

height /if of the hole above the horizontal plane on which 

the projectile strikes, and the distance of its impact, d, beyond 

/i 
the screen. Then tan w = -— nearly. 



38 XX. — EXTERIOR BALLISTICS. 



Or note the inclination of the shot-holes in snow or in 
horizontal targets composed of double layers of boards. 

2. Determine the range OR, figure 15, for a given value 
of Q, and then increase ^ by a slight increment AB. This 
will increase OR by AR = RR\ 

Then assuming HR' to be straight and parallel to the tan- 
gent at R, 

. RR Rt^nAf) 
'^'''^ = RR' = -AR~'''^'^y- 



3. Determine the range under two sets of conditions differ- 
ing only in the height, /i, of the gun above the horizontal 
plane. Then if this difference be relatively small with regard 

to the range from figure 16, tan go = --t-= . 

4. Figure 17 shows how this would practically be done, 
since it would be difficult to raise a gun sufficiently without 
displacing it horizontally : 



tan 6) = 



0' R> — O R. 



Application, 

Range-tables are constructed to give all the principal ele- 
ments of the piece, charge, and trajectory for different ranges.* 

The following method and figure 18 show how, having a 
range-table, we may determine the co-ordinates of the vertex. 

Find in the range-table two angles of departure and of fall 
a and j3, such that their sum =: 6. Then by the principle of 
rigidity S will be the chord to the vertex, and S cos /? = X', 
and 5 sin i3 - Y'. 



* See Chapter XXX, pages 9, 52. 



XX. EXTERIOR, BALLISTICS. 



5. To find the dangerous space at any range, or the hori- 
zontal distance over which a target of given height would be 
struck. 

We have in this case to find the distance at which the height 
of the trajectory is equal to that of the target. The target will 
evidently be struck when situated at this point, since the tra- 
jectory passes through its summit, and it will also be struck 
if situated at any point intermediate between this and the end 
of the range. Hence if D, figure 8, be the target the dan- 
gerous space is DR. 

The simplest way of determining this is as follows. Sup- 
pose the target to be 30 feet high, then from (HI") 

cr;. = O-1067 3 + -T—r = 40626. 4 + 31.9 = 40658. 3 = (T^^^,^ ; 
sm 

or z;, = 1070.9. 
Similarly 

x = DS- 219. 2 ft. = 73 yds. 

If the proper value of w has been found, the same result 
may be obtained by working downward from the vertex, tak- 
ing y = 1576.1 — 30 r= 1546.1, and 

Ovn = (^v. ■ — 7 = CT ,070 3 as before.* 

sm 

The accordance of these methods tests the accuracy of the 
determination of w ; but without exacting the somewhat labo- 
rious process required for this determination, a check of the 
accuracy with which the dangerous space has been determined 
may be had by observing that the angle whose tangent is 
equal to the height of the target divided by the dangerous 
space is greater than and less than w. 



* Or taking the trial values assumed for the descending branch , viz^ 
Vy = 1113 ; J/ ^ = \S24.2'yV yy=z 1061 we have as an approximation 
^ = 1683 J v'^^ =5 1064 ',xs=a 202.6 ft. 



40 XX. — EXTERIOR BALLISTICS. 



The dangerous space is one of the most important proper- 
ties of a trajectory, since, Chap. I, it measures the chances of 
striking an object at a distance which in warfare is only ap- 
proximately known. 

The flatter the trajectory at its further end the greater is the 
permissible margin of error in estimating the range before 
aiming. 

The principles of Chap. XVI and equation (30) illustrate 
the importance of high velocities and high sectional densities, 
since if one projectile, a, figure 19, having less sectional den- 
sity than another, projectile b, be projected with equal ener- 
gies at the same ranges, although the trajectory of a may be 
flatter than that of b at the start, yet near the target the D.S. 
of b will be greater than that of a, if the target lies beyond the 
intersection of the two trajectories. 

Although the method above described is generally followed, 
and is best suited to cases where w is accurately known, a 
simpler and probably a more accurate plan is hereafter given, 
page 44. 

6. To find the time of flight to any distance. Take the 
distance as 1000 yards = 3000 feet, as in \b. We have from 
equation (II) and data previously computed 

/ = (r^. — r^//) ^ = (ri803.9 — ^1097) ^ = 1- '^^03 sec. 

7. To find the time of flight for the whole range. 

1st. We proceed as in No. 3, using equation II and the 
corrected value of v^^ = 1067.3. 

T = (t;/ — r;,//) - = 9.8432 sees, 
and r, = (r;, - nj i = 9.8569 



r=r + T, =19.7001. 



XX. — EXTERIOR BALLISTICS. 41 



2d. Or we may pass directly to the point of fall, as follows: 
rr=(r;.-r7ji= 19.566, 



which is sufficiently accurate for most purposes. 

3d. If the true value of oo or v^^ is not determined, we may 

still approximate to T^ by finding the time 4 required for the 

projectile to pass over the correction of the range determined 

477 
in No. 3, with the velocity u^^ or 4 = — — - = 0.454 sec. 

jLUoU 

Therefore having with the assumed value of cl? = 16° found 
T, = 10.266, its corrected value is 9.812, which added to 7" 
makes T= 19.6552 sees. 

4th. Or, if we neglect the difference in time of passage 
over (y, — Y' )j due to the resistance of the air, since 

/, = \/?(n/k_ v'f), we obtain 4= 0.4186 and T, = 

^ g 
9.8474 which is a closer approximation than 9.812, since 

T, > T! 



Scholium. 
Equation (23), which may be written 

cos g 

or 

gj^ COS0 gj^ COS0 

shows that, although for the descending branch the mean 
value of V is less than that for the ascending branch, the in- 
crease in the value of shown by equation (29), and the con- 
sequent decrease in cos (f>, may compensate and keep the ra- 



42 XX. — EXTERIOR BALLISTICS. 



tio nearly constant ; so that as far as iifue only is concerned 
the trajectory may be supposed to be in vacuo. 

That this is practically so appears from the equality of T 
and T, in the above problem and in those solved by other 
methods. 

Consequently, and particularly for small values of A, when 
the vertical component of the velocity is so small that it may 
be safely neglected, the time to the vertex may be safely taken 
as half the whole time of flight, and in cases of necessity 
Equations (6) and (7) may be employed. 

For example, for this case, which is certainly an extreme 
one, if we substitute the value oi T — 19.70 sec. in the equa- 

tion K = "-^we obtain for Y a value 1561, which is only 

15.2 feet less than that before deduced. When the value of 
A is large, the equations of the trajectory in vacuo cannot be 
indiscriminately applied. 

Principle of the Vertex. 

From the above follows this important conclusion : If we 
represent the time to the vertex by /^ (read / vertex), the ve- 
locity at the vertex by z^y^, and the corresponding time function 

T 

by r^, then /a = y. 

Then we have from equation (II), generalized as to notation, 
Ct. — ^ — '^^LZLEul ~ r ' — r . 



and 






XX. — EXTERIOR BALLISTICS. ^ 43 

Or, the time function of the velocity at the vertex is equal to the 
arithmetical mean of the time functions of the velocities at each 
end of the arc. 

This, which may be termed the principle of the vertex, is of 
great value in approximate solutions. 

If we know the time interval / corresponding to two veloci- 
ties, of which one is known, then the time function of the ver- 
tex of any arc may be determined as follows, from the above 
and Equation (II) : 

Cl , Ct ,^^- 

r A = r^' - Y = -^v" + y . (37) 

8. To find the inclination at the top of the target, which 
we will now assume to be a rampart 30 ft. high, so that what 
was before the dangerous space will be the safe space. 

From equation (I), with the corrected values given, page 37, 
we have 

d=cos(l)iS--6-\l,= -0°, 35674= - 0° 21' 24".*= 



= cos IS 6- \ 77 = 



therefore0 = a7-^ = 15°18'12'"-O°21'24" = 14°56'48". 

Or, working down from the vertex, = 14° 57'. The 
true safe space will, owing to the increasing curvature, be 

30 

somewhat less than ; ., ,o ^r^, = ^^^ ^t- 

tan 14 57 

The difference between this result and that before reached 
for the dangerous space shows the limitations of the ordinary 
method, and is probably due to not having found the correct 
value of for the function d, as explained page 25 and in 
the Appendix. 



41 1 

* = cos T 47' ^2 (^1070. 9 — ^1067. 3) ^. 



44 XX. EXTERIOR BALLISTICS. 

A closer approximation to the dangerous space would 
probably be found from the principle of the vertex, as fol- 
lows: 

Assuming the rigidity of the trajectory, the tangent at the 
vertex of any elementary arc is parallel to the chord. So that, 
finding the inclination 0/^, at the vertex of the arc in rear of the 
target the dangerous space may be found, since 

D.S. = height of target X cot 0/,. 

By using the corrected values pages 37 and 39, 

r -\- T 

w 1070. 8 I 1067. 3 

we find 

V^ = 1069.1, (^,„,,., --(^,„,,.3 = 0°.0260, 

whence 

t/= 0°.1787 and (p^ =15. 30 J - 0.1787 = 15° 7', 47. 

D.S. = 111 feet. 

This method enables us to obtain the dangerous space quite 

closely for an approximate value of v^^ , and to determine an 

important element without requiring the tedious correction 

mentioned, page 37. 

Assuming then v^^ = 1061, the velocity along the tangent is, 
since u^^ = v^^ cos (f) = v„ cos w. 

V,^ cos 

^"^■^^^^ = 1^93, 

the vertical component of which is v,, sin w = 1093 sin 16" = 
301. 

The time of passage over the height of 30 ft. with this ve- 
locity will be / = 0.09961 sec, though it will actually be a trifle 

less, and -- = 0.0071. 

4 



XX. — EXTERIOR BALLISTICS. 45 



Ct 

Now since r^ = 7^./ + - = r,„,, + 0. 0071 = 230. 2330, 

.-. v,^ =: 1061.8. 

Also, since d = cos (c^ioei.e - ^loei)^ = 0.0845, 

30 

d>. = 16° - 0.0845 =15° 54'. 9 and^ = 105 feet. 

^'^ tan 

This is much nearer the true value than the result given by 
the method described page 39. 

Very nearly the result arrived at by the method above de- 
scribed, viz., 105 feet, would be obtained by taking for the time 

of passage / = \J g \ v'1576.2 - |/1546.2l = 0.0947 sec. 

9. Having the initial velocity and the value of C, to find 
the angle of departure necessary to attain a given range, and 
other elements. 

The conditions of this problem, which is a frequent one in 
practice, require (page 6) that the rigidity of the trajectory be 
assumed and that the principle of the vertex be applied. 



Solution. 

1. The piece is supposed to be fired with its axis horizontal, 
and we compute the elements of the trajectory as if it were 
the descending branch of an imaginary trajectory. 

Then we revolve the trajectory upward until the chord 
becomes horizontal. By the principle of rigidity S is 
taken = X, which, to test the accuracy of the method, we 
take = 26517.24 feet, as previously determined. 



-f^'" m THE -)^^:*v 



c 



iiiTh& 



46 XX. — EXTERIOR BALLISTICS. 

From equation (III) we have 

(Tj,^^ = (Tv' — Cx, or v^^ = 1081. 
^rom equation (II) 

^A = i (^,833 + ^:o8i) or v^ = 1348. 
Then from equation (I), since 6 = and cos 0=1, 

d = 1-:^A = 11° 26' 13" = e. 

Compare these results with those previously deduced. 
2. In such a case, to determine the angle of fall and the 
dangerous space, we would proceed as follows : 

Find D, in degrees, the total change = 6 -\- go, hy saying 

■^ = (^:,3. - ^.08:) ^= 26°.29 = 26° 17' 24"; 

then a? = Z> - ^ = 14° 51'. 2 and 
SO 

It is evident from the above, that, knowing the angle of fall 
required to strike near its foot a scarp protected by a cover 
at a known height and separated from it by a ditch of known 
width, it is only necessary to know the distance of the breach- 
ing battery from the wall, and the ballistic coefficient of the 
projectile, to determine approximately the value of 6 and of 
the initial velocity or charge of powder required to strike the 
wall at nearly the desired spot, with a required remaining 
energy. 

It was by some such method that the German artillery 
breached at hitherto unknown ranges the invisible walls of 
Strasburg. See problem page 51. 



XX. — EXTERIOR BALLISTICS. 4? 

Thus, by the principle of rigidity, 

From CX = ay — c^ determine V and weight of charge. 

** CD^Sy- d^ *' D. 

*' conditions ** go. 

** D — GO "6. 

MODIFIED FORMULA. 

For low angles of departure and high velocities and sec- 
tional densities giving small values of A, the principle of 
rigidity permits the formulae on page 28 to be written 

Cd •= Sy — 6^ , (A) 

a = Ty — T^; (B) 

0= ay — (7^,. (C) 

In these formulae, since sin = 0, we must resort to Equa- 
tions (0) and (7) as explained page 7, or 

y=^(T-(): (6) 

y=^^ (7) 

The propriety of this assumption appears from applying it 
to the case of the 100-ton gun, assuming the velocities to be 
horizontal and solving without reference to the vertex. Thus, 
assuming as before (o = 16°, we have from (A), using whole 

numbers, 27°.83 = (6,^ — 6„) ~ .-. 2/,, =1061. 

Similarly we find T= 19.94 sec. and X = 8983 yards, lead- 
ing, as seen by comparison, to but slight errors providing that 
0) has been correctly assumed. 

So that we may have confidence in the results obtained by 
the use of Equations (A), (B), (C), when v does not differ 
much from u , and, when v sin (p is so small that it may be 
neglected, we may use Equations (6) and (7). 



48 XX. — EXTERIOR BALLISTICS. 



Example. 

The Springfield rifle and ammunition give the following 
data : 

W= 500 gr. = 0.071428 lbs. ; 

Diameter of projectile = 0.455 inches in flight • 

V= 1300 ft. 

By experiment we find that for a range of 500 yards as 
measured by the breech sight = 1° 17' 18". 

1. Find GO. 

1st. From (C) determine v^ = 869 

2d. ** (A) " D = 2° 40' 23". 

3d. '* D-d'' fi9 = l°23'05". 

2. Find r. 

1st. From {B) determine T= 1.467 sec. 
2d. " (7) '' i"=8'.662 feet. 

3. Findj^/ at 400 yards = 1200 ft. 

1st. From (C) determine v at 1200 ft. -= 921. 
2d. " (B) " / to 1200 ft. = 1.132 sec. 

3d. " (6) and T above determine 7 = 6.105 ft. 
By this means we may construct a drawing of the tra- 
jectory. 
4 Find the 'Dangerous Space at 500 yards. 
The target is a man 5 ft. 8 in. (5§ ft.) high = y. The gun 
is supposed to be fired lying down (from the ground) and to 
be aimed at the feet of the man. 

1st. Reckoning from the summit of the trajectory we have 

^1 ^ y "~ = 0.4313 for the time from the vertex to 

T 

the top of the man's head, and -^ — /, = time over D. S. = 

0.3022 = f, 

2d From /' and (B) determine v at target = 915. 
3d. From (C) determine D. S. = 267 ft. = 89 yds. 



XX. — EXTERIOR Ballistics. 49 

It is generally 1 etter to work backward from the point of 
fall than forward from the gun, as the results are more con- 
sistent if the data are supplied from only one branch of the 
trajectory. See page 39. 

However, this does not apply in the above case, in which 
the vertical resistance of the air is wholly neglected, so that 
the same results would follow from either course of procedure. 
See page 41. 

Alternate Solution, 

If in Equation (6) we supply the value of T previously 
deduced, and solve the resulting quadratic equation, we shall 
have two values of /, one of which gives the time for the 
projectile to rise to the height of j/, and the other which gives 
the time for the projectile to rise to the vertex and to fall 
to this height above the horizontal plane, so that there will 
be two dangerous spaces, the interval between them being 
the safe space. 

It is evident that as the range decreases, the other conditions 
remaining constant, the safe space finally becomes 0. The 
resulting dangerous space will then be continuous and a 
maximum. 

The maximum dangerous space for a given small-arm thus 
depends upon a physical constant, — the height of a man ; 
and assuming, as above, the mean height of a man to be 5f 
feet, the maximum dangerous space will be a function of p', 
page 23, and will be a convenient measure of the joint power 
of the gun and ammunition. The height i^will = 5f feet. 

5. Find the maximum Dangerous Space for the preceding 
ballistic condidons. 

Sec. 

1st. From (7) determine T= 1.187. 

2d. '' (B) *' z;=912 

3d. '' (C) ** X= 416.6 + yds. = max. D. S. 



50 XX. — EXTERIOR BALLISTICS. 



APPENDIX A. 

The value of was obtained approximately by Mr. Niven 
from an expanding series. (See Proceedings of the Royal 
Society of England, 1887; No. 181.) 

The value of to be used with Table IV for changes of 
inclination is that given in the text for high angles of depart- 
ure, say ^ > 5°. 

For 6* < 5° may be taken =. ^ ~l -. 

For the other tables he takes 

though, where greater approximation is required, for changes 
of time he uses 

APPENDIX B. 

Problems. 

The answers given below result from the use of the modi- 
fied formulae. 

1. The 3.2-inch steel b. 1. rifle. Weight jof shell or shrap- 
nel = 13 lbs. I. V. = 1634. 

Determine : (1) The distance at which v of shrapnel will be 
500. 

(2) Time of flight for this distance. 

(3) Angle of departure for this range, supposing 

the shrapnel to explode 40 ft. above the 
object, or the angle of sight — y'. 
Answers : (1) 19,106 ft. or 3.62 miles. 

(2) 24.6 sec. 

(3) 24'^ 44'. 



XX. — EXTERIOR BALLISTICS. Bl 

2. A target is to be placed on Cro' Nest. The distance 
from the sea-coast battery to target is 1990 yards ; height of 
target above battery is 237 feet. . Determine the angle of 
departure necessary to strike the target, using the 8- inch con- 
verted rifle. ,/ = 7. 95 inches ; 

Weight of projectile = 180 lbs. ; 

I. V =1414. Answer: 5° 45'. 

3. The 6-inch b. 1. rifle requires according to the range 
table an elevation of 1° 51' and a muzzle velocity of 1850 f. s. 
to strike an object at a distance of 2U00 yards. On firing the 
range obtained was only 1800 yards, and investigation showed 
that the powder was damp.* What additional elevation would 
be necessary for a range of 2000 yards ? tV= loo lbs. 

Answer : 0° 28'. 

4. At the siege of Strasbourg in 1870, the Germans wished 
to breach the scarp wall of an outwork at 2000 yards distance ; 
the ditch was known to be 50 feet wide, and the shell were 
to strike 12|- feet below top of counterscarp wall. An 8-inch 
howitzer firing a projectile weighing 180 lbs. with a muzzle 
velocity of 700 f. s. was employed. 

Required the striking velocity and the angle of departure 

A i 616 f. s. 

Answer : i 

(11° 47'. 

5. At a range of 1200 yards a 64-lb. shell grazes the top of 
a traverse 8 feet high. How far beyond the traverse will the 
shot strike the ground ? 

^=6.171 inches; 

Weight of projectile = 64 lbs. ; 

I. V. = 1260 f. s. 

Answer : 153 feet or 51 yards. 

6. A Martini-Henry rifle-bullet strikes a vertical target at 
500 yards at a certain spot when the muzzle velocity is 1353 
f. s. How much lower on the target will the same projectile 

*See proportion, foot p. 7. 



^2 XX. — EXTERIOR BALLISTICS. 

Strike if the muzzle velocity is only 1300 f. s., the elevation 
and other conditions remaining the same ? 

^ = 0.45 inch. 

Weight of projectile == 480 grains = 0.06857 lb. 

Answer : 21|^ inches. 

7. Using the Hebler rifle, determine the maximum con- 
tinuous dangerous space for a man kneeling. 

d =0.296 inch; 
w - 225 grains = 0.03214 lb.; 
I. V. =1942f. s.; 

Height of a man kneeling = 42 inches. 
Compare with Springfield rifle : 
d =0.45 inch ; 
w — 500 grains = 0.07142 lb.; 
I. V. = 1316 f. s. 

Answer: Hebler rifle, 458.0 yards. 
Springfiold rifle, 340.7 '' 

8. A 3-inch Eureka shell, weight 9 lbs., fired with 2 lbs. of 
powder, has an I. V. = 1495 f. s. With what charge should 
a 10-lb. shell be fired to have at 407 yards the same remain- 
ing velocity that the full charge gives at 2500 yards } 

Answer: 11.5 ounces. 

9. A 3.2-inch shell weighing 13 lbs. is fired with a muzzle 
velocity = 958 f. s. The target is at a distance of 407 yards, 
and the angle of sight is 4° 1'. Determine the necessary 
breech-sight elevation and the quadrant elevation. 

Answer: e = V 19'. 
q = b° 20'. 

10. A 3.2-inch shell weighing 13 lbs. is fired with I. V. i= 
986 f- s. How high above the gun should be placed a hori- 
zontal bar at a distance of 80 feet, so that the shell shall 
strike the bar and hit a target on the same level as the gun, 
and at a distance of 1200 yards. Determine also the neces- 
sary breech-sight elevation. 

Answer: Height = 4 ft. 6.5 ins. 
^ = 4° 0' 22'^ 



XX.— EXTERIOR feALLlSTlCS. 



BALLISTIC TABLES. 



Table I. 

Value of K for the Cubic Law of Resistance, Ogival-headed 
Projectiles {1%, diameter heads). 



Velocity. 


Value 
ofK. 


Velocity. 


Value 
OfK. 


Velocity. 


Value 
OfK. 


Velocity. 


Value 
OfK, 


f.8. 




f.s. 




f.s. 




f.s. 




400 .... 


148 





880 .... 


75 





1360 . . . . 


106 


7 


1840 .... 


75 


2 


410 . . . . 


145 


2 


890 .... 


75 





1370 . . . . 


106 


3 


1850 .... 


74 


7 


420 . . . . 


142 


5 


900 .... 


75 





1380 .... 


105 


8 


1860 .... 


74 


2 


430 . . . . 


139 


8 


910 ..:. 


75 





1390 . . . . 


105 


3 


1870 .... 


73 


6 


440 .... 


137 


2 


920 .... 


75 





1400 . . . . 


104 


7 


1880 .... 


73 


1 


4r)0 . . . . 


134 


6 


930 .... 


75 





1410 . . . . 


104 


1 


1890 .... 


72 


6 


460 .... 


132 





940 .... 


75 





1420 . . . . 


103 


5 


1900 .... 


72 


1 


470 . . . . 


129 


4 


950 .... 


75 





1430 . . . . 


102 


9 


1910 .... 


71 


6 


480 .... 


126 


9 


960 .... 


75 





1440 . . . . 


102 


3 


1920 .... 


71 


2 


490 .. . 


124 


4 


970 .... 


75 





1450 . . . . 


101 


6 


1930 .... 


70 


a 


500 . . . . 


121 


9 


980 .... 


75 





1460 . . . . 


100 


9 


1940 .... 


70 


4 


510 . . . . 


119 


6 


990 .... 


75 





1470 . . . . 


100 


1 


1950 .... 


70 





520 . . . . 


117 


3 


1000 .... 


75 





1480 .... 


99 


4 


1960 .... 


69 


7 


530 .... 


115 





1010 .... 


75 


1 


1490 . . . . 


98 


6 


1970 .... 


69 


4 


540 . . . . 


112 


8 


1020 .... 


75 


3 


1500 . . . . 


97 


9 


1980 .... 


69 


2 


550 . . . . 


110 


7 


1030 .... 


76 


7 


1510 . . . . 


97 


1 


1990 .... 


69 





5G0 . . . . 


108 


7 


1040 .... 


80 


8 


1.520 . . . . 


96 


2 


2000 .... 


68 


8 


570 . . . . 


106 


7 


1050 .... 


87 


3 


1530 . . . - 


95 


3 


2010 .... 


68 


6 


580 . . . . 


104 


6 


1060 .... 


94 





1540 . . . . 


94 


4 


2020 .... 


68 


4 


530 . . . . 


102 


5 


1070 .... 


98 


7 


1550 . . . . 


93 


6 


2030 .... 


68 


3 


600 . . . . 


100 


5 


1080 .... 


102 


2 


1560 . . . . 


92 


8 


2040 .... 


68 


2 


610 . . . . 


98 


6 


1090 .... 


104 


9 


1570 


92 





2050 .... 


68 


1 


620 .... 


96 


8 


1100 .... 


lOG 


9 


1580 .... 


91 


2 


2060 .... 


68 





630 . . . . 


95 


1 


1110 .... 


108 


4 


1590 .... 


90 


4 


2070 .... 


67 


9 


640 . . . . 


93 


5 


1120 .... 


109 


2 


1600 .... 


89 


7 


2080 .... 


67 


9 


650 . . . . 


91 


9 


1130 .... 


109 


6 


1610 .... 


89 





2090 .... 


67 


8 


660 . . . . 


90 


5 


1140 .... 


109 


6 


1620 .... 


88 


3 


2100 . . . 


67 


8 


670 . . . . 


89 


1 


1150 .... 


109 


6 


1630 . . . . 


87 


6 


2110 .... 


67 


7 


630 . . . . 


87 


7 


1160 .. . 


109 


6 


1610 . . . . 


86 


9 


2120 .... 


67 


6 


69S .... 


86 


3 


1170 .... 


109 


6 


1650 . . . . 


86 


2 


2130 .... 


67 


6 


700 .... 


84 


9 


1180 .... 


103 


6 


1660 . . . . 


85 


5 


2140 .... 


67 


5 


710 . . . . 


83 


7 


1190 .... 


109 


6 


1670 . . . . 


84 


8 


2150 .... 


67 


4 


720 .... 


82 


6 


1200 .... 


109 


6 


1680 . . . . 


84 


2 


2160 .... 


67 


3 


730 . . . . 


81 


6 


1210 .... 


109 


6 


1690 . . . . 


83 


6 


2170 .... 


67 


2 


740 .... 


80 


6 


1220 .... 


109 


6 


1700 . . . . 


83 





2180 .... 


67 


2 


750 .... 


79 


6 


1230 .... 


109 


5 


1710 . . . . 


82 


4 


2190 .... 


67 


1 


760 .... 


78 


7 


1240 . . . 


103 


5 


1720 .... 


81 


8 


2200 .... 


67 





770 . . . . 


78 





1250 .... 


109 


4 


1730 . . . . 


81 


2 


2210 .... 


66 


9 


780 .... 


77 


4 


12f30 .... 


103 


3 


1740 . . . . 


80 


6 


2220 ... 


66 


8 


790 ... 


76 


8 


1270 .... 


103 


2 


1750 .... 


80 





2230 .... 


66 


8 


800 .... 


76 


2 


1280 .... 


103 





1760 . . . . 


79 


5 


2240 .... 


66 


7 


810 . . . . 


75 


6 


1290 .... 


108 


8 


1770 .... 


78 


9 


22-0 .... 


66 


6 


820 .... 


75 


2 


1300 .... 


108 


6 


1780 .... 


78 


4 


2260 .... 


66 


5 


830 .... 


75 


1 


1310 .... 


lOS 


4 


1700 . . . . 


77 


8 


' 2270 .. 


66 


4 


840 . . . . 


75 





1320 .... 


10^. 


1 


noo .... 


77 


3 


, 2280 .... 


66 


2 


850 . . . . 


75 





1330 .... 


107 


8 


1810 . . . . 


76 


8 


2290 ... 


65 


9 


860 . . . . 


75 





1340 .... 


107 


5 


1820 . . . . 


76 


2 


2300 .... 


65-5 


870 . . . . 


75 


1350 .... 

1 


107 1 


[ 1830 .... 


75-7 







u 



5C5t. — EXTERIOR BALLISTICS. 



Table II. 
Time and Velocity Table, Ct = r^, — r^„. 



V. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Difl: 


f.8. 
40 
41 
42 


20 5-0299 
6-0554 
7 0276 


sees. 
5-1349 
6-1550 
7-1?,'^0 


sees. 
6-2393 
6-2540 
7-2159 


sees. 
5-3432 
6-3525 
7-3093 


sees. 

5-4466 
6-4505 
7-4022 


sees. 
5-5494 
6-5480 
7-4947 


sees. 
6-6517 
6 6450 
7-5867 


sees. 
5-7534 
6-7414 
7-0782 


sees. 

5 8546 

6 8373 
7-7693 


sees. 

6-9553 
6-93^7 
7-8599 


+ 

-1028 
-0975 
-0925 


43 
44 
45 


20 7-9501 
8-8272 
9-6622 


8-0398 
8 9125 
9-7435 


8-1291 
8-9974 
9-8244 


8-2179 
9-0819 
9-9050 


8-3063 
9-1660 
9-9852 


8-3942 
9-2497 
*0-0651 


8-4817 
9-3330 
*0 1446 


8-5687 

9 4159 

*0-2237 


8-6553 
9-4984 
*0-3025 


8-7415 
9-5805 
*0-3809 


-0879 
-0837 
•0799 


46 
47 

48 


21 0-4590 
1-2205 

1-9487 


0-5367 
1.2948 
2-0198 


0-6140 
1 3687 
2-0906 


0-6910 
1-4423 
2 1611 


0-7677 
1-5156 
2-2313 


0-8440 
1-5886 
2-3012 


0-9200 
1 6613 
2-3708 


0-9956 
1-7336 
2-4401 


1-0709 
1-8056 
2-5091 


11459 

1-8773 
2-5779 


-0763 
•0730 
-0699 


40 
60 
61 


21 2-6464 
3-3159 
3-9592 


2-7146 
3-3814 
4-0221 


2-7825 
3-4466 
4-0848 


2-8501 
3-5116 
4 1472 


2-9174 
3 5763 
4-2094 


2-9845 
3-6408 
4 2713 


3 0513 
3-7050 
4-3330 


3-1178 
3-7689 
4-3944 


3-1841 
3 8320 
4-4556 


3-2501 
3-8960 
4-5165 


-0671 
-0645 
-0619 


62 
63 
64 


21 4-5772 
5 1719 
5-7450 


4-6377 
5-2302 
5-8012 


4-6979 

5-2882 
5-8572 


4-7579 
5-3460 
5-9130 


4-8177 
5-4036 
5-9686 


4-8773 
5-4610 
6-0240 


4-9367 
5-5182 
6-0792 


4-9958 
5-5752 
6-1342 


5-0547 
5-6320 
6 1890 


6-1134 
5-6886 
6-2436 


-0596 
-0574 
-0554 


55 
66 
67 


21 6-2980 
6-8311 
7-3460 


6-3522 
6-8834 
7-3965 


6-4062 
6 9355 
7-4469 


6-4600 
6-9874 
7-49-71 


6-5136 
7-0391 
7-5471 


6-5670 
7 0907 
7-5970 


6-6202 
7-1421 
7 6467 


6-6732 
7-1933 
7-6962 


6-7260 
7-2444 
7 7456 


6-7786 
7-2953 
7 7948 


0534 
-0516 
•0499 


68 
69 
60 


21 7-8438 
8-3271 
8 7957 


7-8928 
8 3746 
8-8417 


7 9417 
8-4220 

8 8877 


7-9904 
8-4692 
8-9334 


8-0389 
8-5163 
8-9791 


8-0873 
8-5632 
9 0246 


8-1356 

8 6100 

9 0700 


8-1837 
8-6566 
9 1152 


8-2316 

8 7031 

9 1603 


8-2793 
8-7494 
9 2052 


-0483 
0468 
0454 


61 
62 
63 


21 9 2501 
9-6908 

22 0-1183 


9-2947 
9 7341 
1604 


9 3393 
9-7773 
0-2023 


9 3837 
9-8204 
0-2441 


9-4280 
9-8633 
0-2858 


9-4721 
9-9062 
3273 


9-5161 
9-9489 
0-3687 


9-5600 
9 9914 
4100 


9-6037 
*0-0338 
4512 


9 6473 

*0-0761 

0-4922 


-0441 
0428 
0415 


61 
65 
66 


22 0-5332 
0-9359 
1-3267 


0-5740 
0-9755 
1-3651 


6147 

1 0151 
1-4034 


6552 

1 0544 
1-4416 


0-6957 
1-0937 
1-4797 


0-7360 
1-1328 
1-5177 


0-7762 
1-1718 
1-5555 


0-8163 
1-2107 
1-5933 


0-8563 
1-2495 
1 6309 


0-8962 
1-2881 
1-6684 


-0403 
0391 
■0379 


67 
68 
69 


22 1-7059 
2 0742 
2-4322 


1-7432 
2 1105 
2-4675 


1-7804 
2 1466 
2-5027 


1 8175 
2-1827 
2-5377 


1-8545 
2-2186 
2-5727 


1-8914 
2-2545 
2-6076 


1-9281 
2-2902 
2-6424 


1-9648 

2-3259 
2-6771 


2-0014 
2-3614 
2 7117 


2-0378 
2-3969 
2-7462 


0368 
0358 
0348 


70 
71 

72 


22 2-7806 
3-1196 
3-4492 


2-8150 
3 1530 
3-4816 


2-8492 
3 1863 
3 5140 


2-8833 
3-2195 
3-5462 


2-9174 
3-2526 
3-5784 


2-9513 
3-2856 
3 6105 


2-9852 
3-3185 
3 6424 


3 0189 
3-3513 
3-6743 


3 0526 
3 3840 
3 7061 


3-0862 
3-4167 
3-7378 


0339 
-0330 
-0320 


73 
71 
75 


22 3 7694 
4 0804 
4-3828 


3-8009 
4-1110 
4 4125 


3-8323 
4 1416 
4-4422 


3-8636 
4 1720 
4-4719 


3-8949 
4-2024 
4-5014 


3-9260 
4-2326 
4-5308 


3-9571 

4-2628 
4-5602 


3-9881 
4-2929 
4-5895 


4-0189 
4 3230 
4 6187 


4-0497 
4-3529 
4-6478 


0311 
-0302 
-0294 


76 
77 
78 


22 4-6769 

1 4-9624 

5-2394 


4-7058 
4-9905 
6-2666 


4-7347 
5-0185 
5-2937 


4-7635 
5 0464 
5 3208 


4-7922 
5-0742 
5-3478 


4-8208 
5-1020 
5-3747 


4-8493 
5 ■ 129G 
5-4015 


4-8777 
5 • 1572 
5-4282 


4-9060 
5 1847 
5-4549 


4 9343 
5-2121 

5 4814 


-0286 
•0277 
-0268 


79 
80 
81 


22 5-5079 
5-7685 
6 0214 


5-5343 
5 7941 
6-0463 


5-5606 

5-8197 
6 0711 


5-5869 
5 - 8452 
6-0959 


5-6130 
5-8706 
6-1205 


6-6391 
5-8959 
6-1451 


5-6652 
5-9212 
6-1696 


5-6911 
5-9463 
6-1941 


5-7170 
5-9714 
6-2184 


5-7428 
5-9965 
6-2427 


-0261 
-0253 
-0245 


82 
83 
84 


22 6-2669 
6-5044 
6-7337 


6-2910 
6-5277 
6-7562 


6 3151 
6-5509 
6-7786 


6-3390 
6 5740 
6-8009 


6-3629 

6-5971 
6-8232 


6-3867 
6 6201 
6-8454 


6-4104 
6 6430 
6-8675 


6-4340 
6 6658 
6-8895 


6-4576 
6-6885 
6-9114 


6 4810 
6-7111 
6 9333 


0237 
0229 
-0221 


85 
86 


22 6-9551 

■7- 1688 
7-3752 


6-9768 

7-1898 
7-3954 


6-9984 

7-2107 
7 -U5G 


7 0200 

7 ■ 2:315 
7-43J7 


7 -0415 

7-2522 
7-4358 


7-0629 
7-2729 

7-4757 


7 -0842 
7-2935 
7-4956 


7-1055 
7 3140 
7-5155 


7 -1267 
7-3345 
7 5353 


7-1478 
7-3549 


-0214 
-0206 
0199 



XX. — EXTERIOR BALLISTICS. 



55 



Table II. — Continued. 
Time and Velocity Table, Gt — r^, 



22 7 
7 
7 

22 8 



22 8 



22 9 
9 
9 

22 9 



22 9 

23 


23 



23 



23 



23 



23 1 
•1 

1 

23 1 

1 
1 

23 1 

1 
1 

23 1 

1 
1 

23 1 
1 

1 



5746 
7677 
9544 

1346 
3090 
4778 

6411 
7994 
9528 

1014 
2454 
3851 

5207 
6522 
7796 

9024 
0177 
1226 

2170 
3031 
3835 

4593 
5314 



6668 
7311 



8545 
9142 
9720 

0283 
0832 
1367 



3381 
3855 
4318 

4771 
5214 
5647 

6071 
6486 
6893 



23 1 7291 
1-7682 
1-8066 



5942 
7866 
9727 

1523 
3261 
4943 

6572 
8150 
9678 

1160 
2596 



5340 
6651 
7921 

9144 
0287 
1325 



3114 
3913 

4667 
5384 
6071 

6733 

7374 
7997 

8605 
9200 
9777 

0338 
0886 
1420 

1941 
2449 
2945 

3429 
3902 
4364 

4816 
5257 
5690 

6113 
6527 
6933 

7331 
7721 
8104 



6137 
8055 



1699 
3432 
5109 

6732 
8305 



1306 

2737 
4126 

5473 
6780 
8046 

9262 
0396 
1423 



4740 
5454 
6139 

6798 
7437 
8059 

8665 
9259 



0394 
0940 
1473 

1992 
2499 
2994 

3477 
3948 
4410 

4860 
5301 
5732 

6155 
6568 



7370 
7760 
8142 



2347 
3196 




6332 
8244 
0091 

1875 
3602 
5273 



8459 
9978 

1451 

2878 
4262 

5606 
6C08 
8170 



0504 
1520 

2435 
3278 
4067 

4813 
5524 
6206 

6863 
7500 
8120 

8726 
9317 



0449 
0934 
1525 



2549 
3043 

3524 
3995 
4455 

4905 
5345 
5775 

6196 
6609 
7013 

7410 

7798 
8179 



6526 
8431 
0272 

2050 
3772 
5437 

7051 
8613 
0128 

1595 
3018 
4398 

5738 
7036 
8294 

9496 
0610 
1615 

2522 
3359 
4143 

4885 
5593 



7563 
8181 

8787 
9375 
9947 

0504 

1048 
1578 



1-2095 
1-2599 
1 3091 



3572 
4041 
4501 

4949 
5388 
5818 



7449 
7837 
8217 



6719 



sees. 

7- 



0452 j 8 

2225 ! 8 

3941 8 
5601 



7209 
8767 
0276 



1740 ' 9 
3158 ! 9 
4534 9 



7164 
8417 

9612 
071G 
1710 
















1 

1 
1 
1 

1 
1 
1 

1 

1 
1 

1 
1 
1 

1 
1 

1 

1 
1 
1 



3439 
4219 

4958 
5662 
6339 



7625 
8242 

8847 
9433 
0003 

0559 
1101 
1630 

2146 
2649 
3140 

3619 
4088 
4546 



7875 
8255 



6912 



0632 



4109 
5764 

7367 
8920 
0425 

1884 
3298 
4670 

6001 

7291 
8540 

9727 
0820 
1804 

2694 
3520 
4295 



5731 
6405 



7056 

7688 



9490 
0059 

0614 
1154 
1682 

2196 
2698 



4134 
4591 



5475 
5902 

6321 
6731 
7133 

7527 
7913 
8292 



7 


9 


9 


sees. 
7-7104 
7-8991 
8-0812 


sees. 
7 7295 
7 9176 
8-0990 


sees. 
7 7486 

7 9360 

8 1168 


8-2573 
8 4277 
8 5927 


8 2746 
8-4445 
8-6089 


8-2918 
8-4611 
8 6250 


8-7525 
8 9073 
9-0573 


8-7682 
8-9225 
9 0720 


8-7838 

8 9376 

9 0867 


9 2027 
9-3437 
9-4805 


9-2170 
9 3575 
9-4939 


9 2312 
9 3713 
9 5073 


9-6132 
9-7418 
9-8662 


9-6262 
9-7544 
9-8783 


9-6392 
9 7670 
9 8904 


9-9841 
0923 
0-1897 


9-9954 
1025 
1988 


*0 0066 
1126 
0-2079 


0-2780 
3599 
4370 


0-2864 
0-3678 
0-4445 


2948 
3757 
4519 


0-5101 
5800 
6471 


0-5172 
0-5868 
6537 


0-5243 
5936 
6603 


0-7120 
7750 
0-8364 


0-7184 
7812 
8424 


0-7248 
0-7874 
0-8484 


0-8965 
0-9648 
1-0115 


9024 
9605 
1-0171 


9083 

9663 

1 0227 


10669 
1-1208 
11734 


1 0723 
1-1261 
1 1786 


10778 
1-1314 
1-1838 


1-2247 
1-2748 
1 3237 


1-2298 
1 2797 
1-3285 


1-2348 
1-2847 
1 3333 


1 3714 
1-4180 
1-4636 


1-3761 
1 4226 
1-4681 


1-3808 
1-4272 
1-4726 


1-6082 
1-5518 
1-5945 


1-5126 
1-5561 
1-5987 


1 5170 
1 5604 
1-6029 


1-6362 
1-6772 
1-7173 


1 6404 
1-6812 
1 7212 


1 6445 
1-6852 
1 7252 


1 7566 
1-7952 
1 8330 


1 7605 
1-7990 
1-8367 


1-7644 
1-8028 
1-8405 



m 



X5t. — EXTERIOR BALLISTICS. 



Table II. — Continued. 
Time and Velocity Table, Ct = r 



23 1 

1 



23 2 
2 
2 



23 2 
2 
2 



23 2 
2 



23 2 
2 
2 



23 2 
2 
2 



23 2 
2 
2 



23 2 
2 

2 

23 2 
2 
2 



23 2 
2 
2 

23 2 



23 2 
2 
2 

23 2 



23 3 
3 
3 



23 



8442 
8812 
9175 

9532 
9883 
0228 

0569 
0904 
1234 



2197 

2509 
2818 
3123 

3424 
3722 
4016 

4308 

4597 
4882 

5165 
5444 
5721 

5994 
62G5 
6533 

6798 
7061 
7320 

7577 
7832 
8084 

8333 

8580 
8824 

9065 
9304 
9541 

9776 
0008 
0237 

0465 
0690 
0913 

1134 
1353 
1569 



•8479 
•8848 
•9211 


!•{ 
1^{ 
1 < 


•9567 
•9918 
•0263 


1^{ 
!•' 
2 ( 


0602 
•0937 
•1267 


2 ( 
2( 
2 ] 


•1591 
•1912 
•2228 


2 ] 
2 ] 
2 5 


•2540 
•2849 
•3153 


2-' 
2' 
2- 


•3454 
•3751 
•4046 


2- 
2- 
2 


•4337 
■4625 
•4911 


2- 

2- 
2- 


•5193 
•5472 
•5748 


2- 
2- 
2- 


•6022 
•6292 
•6560 


2- 
2- 
2 


•6825 
•7087 
7346 


2- 
2- 
2- 


•7603 

•7857 
•8109 


2 
2- 
2- 


•8358 
•8604 
•8848 


2 
2- 
2- 


•9089 
•9328 
•9565 


2- 
2- 
2- 


•9799 
J 0031 
5 0260 


2- 
3- 
3- 


r0488 
J 0713 
{•0935 


3 
3^ 
3- 


$1156 
$1375 
J 1591 


3 
3 
3- 



•8517 
•8885 
•9247 

•9602 
•9952 
•0297 



•0636 
•0970 
•1299 

•1624 
•1944 
•2260 

•2571 

■2879 



•3484 
•3781 
•4075 

•4366 
•4654 
•4939 

•5221 
•5500 
•5776 

•6049 
•6319 



•6851 
•7113 
•7372 

•7628 
•7882 
•8134 



•8629 
•8872 



•9113 
•9352 



•9822 
0054 



0510 
•0735 
■0958 

1178 
1396 
•1613 



8554 
8921 
9282 

9638 
9987 
0331 

0670 
1003 
1332 

1656 
1975 
2291 

2602 
2910 
3214 

3514 
3810 
4104 

4395 
4683 
4967 

5249 
5528 



6076 
6346 



6877 
7139 
7398 

7654 
7908 
8159 

8407 
8653 



2 9137 
2 

2 9612 

2-9845 

3 0077 
3 0306 

3 0533 
3 0757 



3 1200 
3 1418 
3 1634 



8591 
8958 
9318 

9673 
0022 
0365 

0703 
1036 
1364 

1688 
2007 
2322 

2633 
2940 
3244 

3543 
3840 
4133 

4424 
4711 
4996 

5277 
5555 
5831 



6373 
6640 



7165 
7423 

7679 
7933 
8184 

8432 
8678 
8921 

9161 
9399 
9635 



0100 
0329 

0555 
0780 
1002 

1222 
1440 
1656 



8628 
8994 
9354 

9708 
0056 
0399 

0737 
1069 
1397 

1720 
2039 
2354 

2664 
2971 
3274 

3573 
3869 
4162 

4453 
4740 
5024 

5305 

5583 
5858 

6130 
6400 
6666 



7191 
7449 

7705 
7958 
8209 

8457 
8702 



9185 
9423 
9659 

9892 
0123 
0351 

0578 
0802 
1024 

1244 
1461 
1677 



8665 
9030 



9743 
0091 
0433 

0770 
1102 
1430 

1752 
2071 
2385 

2695 
3001 
3304 



3899 
4192 

4481 
4768 
5052 

5333 
5611 



6157 
6426 



6956 
7217 

7475 

7730 
7983 
8234 

8481 
8726 



9209 
9447 
9682 

9915 
0146 
0374 

0600 
0824 
1045 

1266 
1483 
1698 



8702 
9067 
9425 

9778 
0125 
0467 



1135 
1462 

1784 
2102 
2416 

2726 
3032 



3928 
4221 

4510 

4797 
5080 

5361 
5638 
5913 

6184 
6453 
6719 

6982 
7243 
7500 

7756 
8008 
8258 

8506 

8751 



9470 
9705 

9938 
0169 
0397 

0623 
0847 
1068 

1287 
1505 
1720 



8738 
9103 
9461 

9813 
0160 
0501 



1168 
1494 

1816 
2134 
2447 

2757 
3062 



3958 
4250 

4539 

4825 
5108 



5666 
5940 

6211 
6480 
6745 

7008 
7268 
7526 

7781 
8034 
8283 

8531 

8775 
9017 

9257 
9494 
9729 

9961 
0192 
0420 

0645 
0869 
1090 

1309 
1526 
1741 



8775 
9139 



•9848 
0194 
0535 

0870 
1201 
1527 

1848 
2165 
2478 

2787 
3093 
3394 

3692 
3987 
4279 

4568 
4854 
5137 

5416 
5693 
5967 

6238 
6506 
6772 

7034 
7294 
7552 

7806 
8059 
8308 

8555 
8799 
9041 

•9281 
•9518 
•9752 



0215 
0442 

0668 
0891 
1112 



XX. — EXTERIOR BALLISTICS. 



57 



Table II. — Continued. 
Time and Velocity Table, Ct = r^, — r^„ 



V. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


f.R. 
184 

185 
18G 


sees. 
23 3 1784 
3 1997 
3 2207 


Bees. 
3 1805 
3-2018 
3-2228 


sees. 
3 ■ 1827 
3 2039 
3-2249 


g 
3 
3 
3 


ecs. 
1848 
2060 
2270 


sees. 
3-1869 
3-2081 
3-2291 


s 
3 
3 
3 


eca. 

1891 
2102 
2312 


sees. 
3-1012 
3-2123 
3-2333 


sees. 

3 1033 
3-2144 
3-2353 


8 
3 
3 
3 


ecs. 
1954 
2165 
2374 


sees. 
3-1975 
3-2186 
3-2395 


+ 

•0021 
-C021 

0021 


187 
188 
139 


23 3 2416 
3-2623 
3-2828 


3-2437 
3-2643 
3-2848 


3 2457 
3-2664 
3-2869 


3 
3 
3 


2478 
2683 
2889 


3-2499 
3-2705 
3-2909 


3 

3 
3 


2520 

2726 
2930 


3 2540 
3-2746 
3-2950 


3-2561 
3 2767 
3-2970 


3 
3 
3 


2582 
2787 
2091 


3-2602 
3-2803 
3-3011 


-0021 
-0021 
0020 


100 
191 
102 


23 3-3031 
3-3233 
3-3432 


3-3051 
3-3253 
3-3452 


3-3072 
3-3273 
3 3472 


3 
3 
3 


3092 
3293 
3492 


3-3112 
3-3313 
3-3511 


3 
3 
3 


3132 

3333 
3531 


3-3152 
3-3353 
3-3551 


3-3172 
3 3372 
3-3571 


8 

3 
3 


3102 
3302 
3500 


3-3212 
3-3412 
3-3G10 


-0020 
-0020 
-0020 


193 
104 
105 


23 3-3630 
3-3825 
3 4019 


3-3649 
3 3845 
3 4038 


3-3669 
3-3864 
3-4057 


3 
3 
3 


3689 
3884 
4077 


3-3708 
3 3903 
3 4096 


3 
3 
3 


3728 
3922 
4115 


3-3747 
3-3942 
3 4134 


3-3767 
3-3061 
3 4153 


3 
3 
3 


3786 
3080 
4172 


3-3806 
3 4000 
3-4192 


-0020 
0019 
0019 


IOC 

107 
108 


23 3 4211 
3 4400 
3-4588 


3-4230 
3-4419 
3 4606 


3-4240 
3-4438 
3-4625 


3 
3 
3 


4268 
4457 
4644 


3-4287 
3 4476 
3-4662 


3 
3 
3 


4306 
4494 
4681 


3-4325 
3-4513 
3-4699 


3 4344 
3-4532 
3-4718 


3 
3 
3 


4362 
4550 
4736 


8-4381 
3-45C9 
3-4755 


0019 
0019 
0019 


100 
200 
201 


23 3 4773 
3-4956 
3-5137 


3 4791 
3-4074 
3 5155 


3-4810 
3-4002 
3-5172 


3 
3 
3 


4828 
5010 
5190 


3-4846 
3-5028 
3 5208 


3 
3 
3 


4865 
5047 
5226 


3-4883 
3-5065 
3 5244 


3-4901 
8-5083 
3-5262 


3 
3 
3 


4920 
5101 
5280 


3-4938 
3-5119 
3-5297 


-0018 
0018 
0018 


202 

203 
204 


23 3-5315 
3-5402 
3-5666 


3-5333 
3-5500 
3-5683 


3-5351 
3-5527 
3-5700 


3 
3 
3 


5368 
5544 
5717 


3-5386 
3-5561 
3 5735 


3 
3 
3 


5404 
5579 
5752 


3-5421 
3-5596 
3-5769 


3-5439 
3-5614 
3-5786 


3 
3 
3 


5456 
5631 
5803 


8-5474 
3-5648 
3 5820 


0018 
•0017 
0017 


205 
208 
207 


23 3-5837 
3 6007 
3-6174 


3-5854 
3-6024 
3 6191 


3-5871 
3-6040 
3-6207 


3 
3 
3 


5888 
6057 
6224 


3 5905 
3-6074 
3 6240 


3 
3 
3 


5922 
6091 
6257 


3-5939 
3-6107 
3-6273 


3 5956 
3-6124 
3-6290 


8 
3 
3 


5973 
6141 
6306 


3-5990 
3-6157 
3 6323 


0017 
-0017 
-0016 


203 

2O0 
210 


23 3 6339 
3 6502 
3-6662 


3-6355 

3-6518 
3 -6078 


3-6372 
3-6534 
3-6694 


3 
3 
3 


6388 
6550 
6710 


3 6404 
3-6566 
3-6726 


3 
3 
3 


6420 
6582 
6741 


3-6437 
3-6598 
3-6757 


3-6453 
3-6614 
3-6773 


3 

3 
3 


6469 
6630 
6789 


8 6485 
3-6646 
3 6805 


-0016 
0016 
0016 


211 

212 
213 


23 3-6820 
3-6977 
3-7131 


3 6836 
3-6902 
3-7146 


3-6852 
3-7008 
3-7162 


3 
3 
3 


6867 
7023 
7177 


3-6883 
3-7039 
3-7192 


3 
3 
3 


6899 
7054 
7207 


3-6914 
3 7070 
3 7223 


3-6930 

3-7085 
3-7238 


3 
3 
3 


6946 
7100 
7253 


8-6961 
3-7116 
3-7268 


0016 
•0015 
0015 


214 
215 
216 


23 3-7283 
3-7434 
3-7582 


3-7298 
3 7448 
3-7597 


3 7313 

3 -7463 
3 7612 


3 
3 
3 


7329 

7478 
7626 


3 7344 
3-7493 
3 7641 


3 
3 
3 


7359 
7508 
7656 


3-7374 
3-7523 
3 7670 


3-7389 
3-7538 
3-7685 


3 
3 
3 


7404 

7552 
7700 


3-7419 
3-7567 
3-7714 


0015 
0015 
-0015 


217 
218 
210 


23 3 7729 
3-7874 
3-8016 


3 7743 

3 7888 
3 8031 


3-7758 
3 7002 
3 8045 


3 
3 
3 


7772 
7917 
8059 


3-7787 
3-7931 
3 8073 


3 
3 
3 


7801 
7945 
8087 


3-7816 
3-79G0 
3-8101 


3-7830 
3-7974 
3 8115 


3 
3 
3 


7845 
7988 
8129 


3-7859 
3 8002 
3-8144 


0014 
OOU 
0014 


220 
221 
222 


23 3-8158 
3-8297 
3 8435 


3-8372 
3 8311 
3 8448 


3 8186 
3-8325 
3 8462 


3 
3 
3 


8200 

8338 
8476 


8-8214 
3 8352 
3 8489 


3 
3 
3 


8227 
8366 
8503 


3-8241 
3-8380 
3 8517 


3-8255 
3 8394 
3 8530 


3 
3 


8269 
8407 
8544 


8 8283 
3-8421 
3-8557 


0014 
0014 
0014 


223 
224 

225 


23 3-8571 
3-8705 

3-8838 


3-8584 
3-8718 
3-8851 


3 8508 
3-8732 
3-8864 


3 
3 
3 


8611 
8745 
8877 


3-8625 
3-8758 
3-8890 


3 
3 
3 


8638 
8772 
8903 


3-8651 

3-8785 
3 8916 


3-8665 
3-8798 
3-8930 


3 
3 
3 


8678 
8811 
8943 


8-8692 
3 8824 
3-8956 


i ooia 

0013 
-0013 


226 
227 
228 


23 3 8969 
3 00'^« 
3-922G 


3-8982 
3-9111 
3 92u9 


3-8995 
3 9124 
3-9252 


3 
3 

3 


-9008 
-9137 
9264 


3-9021 
3-9150 

3-9277 


3 
3 

3 


9034 
9162 
9290 


3-9047 
3-9175 
3 y..03 


3-9059 
3-91R8 
3 9315 


3 
3 
3 


9072 
9201 
-9323 


3-9085 
3-9214 
3 9341 


001& 
0013 
•0013 


229 
230 


23 3-9353 
3 9470 


3-9366 
3-9i92 


3-937S 

3- 0:01 


3 


-9301 
-9517 


3 9401 
3 -2029 


3 


9*15 


' 3-9429 
3-9554 


3-9441 
3-9507 


8 
3 


-9454 
9579 


3-9467 
3-9592 


0013 
0013 



58 



XX. EXTERIOR BALLISTICS. 



Table III 

Distance and Velocity Table, Cs = c^ — (7^/,. 



feet. 

2 5008 

5424 

5827 



2 6219 
6601 
6972 

2 7335 
7688 
8034 

2 8373 
8704 
9029 

2 9347 
9659 
9966 

3 0267 
0.563 

. 0854 

3 1140 
1423 
1701 

3 1076 

2247 

- 2514 

3 2777 
3037 
3292 

3 3544 
3793 
4038 

3 4280 
4519 
4754 

3 4986 
5215 
5440 

3 5662 
5S80 
6094 

3 6305 
6512 
6716 

3 6916 
7111 
7303 

3 74nO 

7672 
7850 



feet. 
5050 2 
5464-9 
5867-3 



6258 
6638 
7009 

7370 
7723 
8068 

8406 
8737 
9061 



9690 



0297 
0592 



1169 
1451 
1729 



7 

2274 
2540 8 



3318 

3569 
3818 
4062 

4304 
4543 

4777 

5009 
5237 
5462 

5684 
5902 
6116 

6326 
6533 



7 
5 

1 

1 

4 
1 
6736 3 

6935 7 
7131 
7322 

7^0'^ -5 
7690-5 
7868-2 



feet. 
5092 
5505 
5903 



6296 
6676 
7046 

7406 
7758 
8103 

8439 
8769 
9093 

9410 
9721 
0027 

0327 
0622 
0912 

1197 
1479 
1757 

2031 
2301 

2567 

2829 
3038 
3343 

3594 

3842 
4087 

4328 
4566 
4801 

5032 
52G0 
5484 

5706 
5923 
6137 

6347 
6553 
6756 

6955 
7150 
7340 

7526 
7708 
7885 



feet. 
5134 
5546 
5946 



6335 
6713 
7082 

7442 
7793 
8137 

8473 
8802 
9125 

9441 
9752 
^0057 

0357 
0651 
0940 

1226 
1507 

1784 

2058 
2327 



2855 
3114 



3619 
3867 
4111 

4352 
4590 



5055 
5282 
5507 

5728 
5945 
6158 

6368 
6574 
6776 

6975 
7169 
7359 

7.^45 
7726 
7903 



feet. 

5176 
5586 
5985 



' 6373 
6751 

I 7118 

I 

: 7477 
7828 

1 8170 



8835 
9157 



6 9472 

2 9783 

3 *0087 



0386 
0680 



9 , 0969 



1254 
1535 
1812 



2354 
2020 

28S1 
3139 
3394 

3644 
3891 
4135 

4376 
4613 

4847 

5078 
5305 
5529 

5749 
5966 
6179 



6594 
6796 

6994 

7188 
7378 



3 7563 

4 7744 
3 ' 7920 

I 



feet. 

5217 
5627 
6025 



6411 

6788 
7155 

7513 
7862 
8204 

8539 

8867 
9189 

9504 
9813 
mi7 

0416 
0709 
0998 

1282 
1563 
1839 

2112 

2381 
2646 

2907 
3165 
3419 

3669 
3916 
4159 

4400 
4637 
4871 

5101 

5328 
5551 

5771 
5988 
6200 

6409 
6614 
6816 

7014 
7207 
7397 

7581 
7762 
7938 



feet. 

5259 
5667 
6064 



6449 
6825 
7191 

7548 
7897 



8572 
8900 
9220 

9535 
9844 
"^0147 

0445 
0738 
1026 

1310 
1590 

1867 

2139 
2407 
2672 

2933 
3191 
3444 

3694 
3940 
4184 

4424 
4660 
4894 

5124 
5350 
5573 

5793 
6009 
6221 

6430 
6635 



7033 
7227 
7415 

7600 
7779 
7955 



feet. 

5300 
5707 
6103 



6487 
6862 
7227 

7583 
7931 
8272 



8932 
9252 

9566 
9874 
'^0177 

0475 
0767 
1055 

1339 

1618 
1894 

2166 
2434 



2959 
3216 
3469 

3719 
3965 
4208 



5815 
6030 
6242 

64.50 
6655 
6856 

7053 

7246 
7434 

7618 
7797 
7973 



4448 -0 
4684-4 

4917-4 

5146 9 
5373 
5595 



feet. 
5341 
5747 
6142 

6525 
6899 
7263 



7618 
7966 
8305 



8964 
9284 

9597 
9905 
'0207 

0504 
0796 



1367 
1646 
1921 

2193 
2461 
2725 



2985-4 
3242 
3494 7 

3743 
3989 
4232 



4471 
4707 
4940 

5169 
5395 
5617 

5837 
6052 
6263 

6471 

6675 
6876 

7072 

7265 
7453 

7636 
7815 
7990 



feet. 

5383 
5787 8 
6181 

6563-6 
6936 1 
7299-2 

7653-9 



8000 



8671 
8996 
9315 

9628 
9935 
^0237 

0534 
0825 
1112 

1395 

1674 
1949 

2220 
2487 
2751 

3011 

3267 
3519 

3768 
4014 
4256 

4495 
4731 
4963 

, 5192 

! 5417 

5640 



5858-7 
6073-6 
6284 6 

6492 



7092 

7284 
7471 

76.54 
7833 
8007 



XX — EXTERIOR BALLISTICS. 



Table III. — Continued. 
Distance and Velocity Table, Cs = o-^, — cr^,,. 



V. 





1 


2 


3 


4 


6 


6 


7 


8 


9 


Dim 


88 
89 
90 


feet. 
3 8024-8 
8195 
8361-5 


feet. 
8042 
8211-9 
8377-9 


feet. 

8059 2 
8228-6 
8394-3 


feet. 
8076.3 
8245 4 
8410-7 


feet. 
8093-4 
8262-1 
8427-0 


feet. 
8110-4 
8278-7 
8443-3 


feet. 

8127-4 
8295-4 
8459-6 


feet. 
8144-4 
8312-0 
8475-8 


feet. 
8161 3 
8328-5 
8492-0 


feet. 
8178-2 
8345-0 
8508-2 


+ 

17-0 
16 6 
16-3 


91 
92 
93 


3 8524-3 
8683-5 
8839-4 


8540 4 
8699-3 
8854-8 


8556-4 
8715-0 
8870-2 


8572-4 
8730-7 
8885-5 


8588-4 
8746-3 
8900-8 


8604-3 
8761-9 
8916-1 


8620-3 
8777-5 
8931-3 


8636-1 
8793-0 
8946-5 


8652-0 
8808-5 
8961-7 


8667-8 
8824-0 
8976-8 


15 9 
15-6 
15 3 


94 
95 
96 


3 8991-9 
9141 2 
9287 4 


9007-0 
9156 
9301-9 


9022-0 
9170-7 
9316 3 


9037-0 
9185-4 
9330-7 


9052-0 
9200 1 
9345 


9066-9 
9214-7 
9359-4 


9081-9 
9229-3 
9373-7 


9096-7 
9243-9 
9387-9 


9111-6 
9258 4 
9402-2 


9126-4 
9272-9 
9416-4 


15 
14-6 
14-3 


97 
98 
99 


3 9430 6 
9570 8 
9708-3 


9444-7 
9584-7 
9721-9 


9458 9 
9598-6 
9735-4 


9473-0 
9612-4 
9749-0 


9487-0 
9626 1 
9762-5 


9.501-1 
9639-9 
9775-9 


9.515-1 
96.53-6 
9789-4 


9529 1 
9667-3 
9802-8 


9543-0 
9681-0 
9816-2 


9557-0 
9604-6 
9829-6 


14 
13-7 
13-5 


100 
101 
102 


3 9842 9 
9975 

4 0104 3 


9856 3 
9988 1 
0117 1 


9869-6 
*0001-1 
0129 8 


9882-9 
*()014-1 
0142-5 


9896-1 
*0027-l 
0155-2 


9909-3 

:*0040-0 

0167-8 


9922-5 
*00.52-9 
0180-4 


9935-3 

*0065-8 
0192 9 


9948 8 
*0078-7 
0-205 4 


9961-9 
*009l-5 
0217-8 


13-2 
12-9 
12-6 


103 
104 
105 


4 0230-1 
0349 4 
0459-2 


0242 4 
0360-8 
0469 6 


0254-6 
0372-2 
0479-9 


0266-8 
0383-4 
0490-0 


0278-8 
0394-5 
0500-1 


0290-8 
0405-6 
0510 1 


0302-7 
0416-5 
0520 


0314 5 
0427-3 
0529-8 


0326-2 
0438-1 
0539 5 


0337-8 
0448-7 
0549-2 


11 9 
11-0 
9-9 


106 
107 
108 


4 0558 7 
0650 5 
0736-8 


0568-2 
0659-3 
0745 2 


0577 6 
0668 1 
0753 6 


0.586-9 
0676-9 
0761-9 


0596 2 
0685-6 
0770-2 


0605-4 
0G94-2 
0778-4 


0614-5 
0702-8 
0786-6 


0623-6 
0711-4 
0794-8 


0632-6 
0719-9 
0802-9 


0641-6 
0728-4 
0811-0 


9 2 
8 6 
8-2 


109 ' 

110 

111 


4 0819 
0897-9 
0974-2 


0827-1 
0905 7 
0981 6 


0835 
0913-4 
0989 1 


0843-0 
0921-1 
0996 6 


0850-9 
0928-7 
1004-0 


0858-9 
0936-4 
1011-4 


0866-7 
0944-0 
1018-8 


0874-6 
09.51-5 
1026 2 


0882-4 
0959 1 
1033-5 


089(r 
0966 
1040 


2 
6 
9 


7-9 

7-6 

7-4 


112 
113 
lU 


4 1048 2 
1120 5 
1191 4 


1055-5 
1127-6 
1198-4 


1062-8 
1134-8 
1205-4 


1070 
1141 9 
1212 4 


1077-3 
1149-0 
1219-4 


1084-5 
1156-1 
1226-4 


1091-7 
1163 2 
1233 3 


1099 
1170 2 
1240 3 


1106-1 
1177-3 
1247-2 


1113 
1184 
1254 


3 

4 

1 


7-2 
71 
6 9 


115 
116 

117 1 


4 1261 
1329-5 
1396 8 


1267-9 
1336 3 
1403-5 


1274-8 
1343-1 
1410 1 


1281-7 
1349 8 
1416-8 


1288-6 
1356 6 
1423-4 


1295-4 
1363-3 
1430 


1302-3 
1370 
1436-6 


1309 1 
1376-7 
1443-2 


1315-9 

1383-4 
1449-8 


1322 
1390 
1456 


7 
1 
4 


6 8 
6 7 
66 


118 
119 i 
120 


4 1462 9 
1528-0 
1591 9 


1469 5 
1534-4 
1598-3 


1476-0 
1540 9 
1604-6 


1482 6 
1547-3 
1610-9 


1489-1 
1553-7 
1617-2 


1495-6 
1.560-1 
1623-5 


1502 1 
1566-5 
1629-8 


1508 6 
1572-9 
1636-1 


1515-1 
1,579-2 
1642-3 


1521 
1585 
1648 


5 
6 
6 


6 5 
6-4 
6 3 


121 
122 
123 


4 1654-8 
1716 7 
1777-5 


1661 1 

1722-8 
1783 6 


l«67-3 
1728-8 
1789-6 


1673-5 
1735 
1795-6 


1679-7 
1741 1 
1801 6 


1685-9 

1747-2 
1807-6 


1692-1 
1753 3 
1813-6 


1698-2 
1759-4 
1819-6 


1704-4 
1765 4 
1825 6 


1710 

1771 
1831 


5 
5 
5 


6-2 
6-1 
6 


124 

125 1 
126 


4 1837 5 
1896 5 
1954-6 


1843 4 
1902 3 
1960 4 


1849-4 
1908-2 
1966-1 


1855-3 
1914 
1971-9 


1861-2 
1919-8 
1977 6 


1867-1 
1925-6 
1983 3 


1873-0 
1931-5 
1989-0 


1878-9 
1937-3 
1994-8 


1884-8 
1943 
2000 5 


1890 
1948 
2006 


6 
8 
2 


5 9 

5 8 

5-7 


127 
128 
129 


4 2011-8 
2068-3 
21-23-9 


2017-5 
2073-9 
2129-4 


2023-2 
2079 5 
2135 


2028-9 
2085-0 
2140 5 


2034-5 
2090-6 
2146-0 


2040-2 
2096-2 
2151-5 


2045-8 
2101 8 
2157-0 


2051-4 
2107-3 
2162-4 


2057 
2112-9 
2167-9 


2062 
2118 
2173 


7 
4 
4 


5-6 
5-6 
5-5 


130 
131 
132 


4 2178-8 
2233 
2286 4 


2184-3 
2238-4 
2291-8 


2189-7 
2243-7 
2297-1 


2195-1 
2249-1 
2302-4 


2200-6 
2254-5 
2307-6 


2206 

22.59-8 
2312 9 


2211-4 
2265-1 
2318-2 


2216-8 
2270-5 
2323 5 


2222-2 
2275-8 
2328-7 


2227 
2281 
2334 


6 
1 



5-4 
5 3 
53 


133 
134 
135 


4 2339-2 
2391-4 
2443 


2344-5 
2396 6 
2448-1 


2349-7 
2401 8 
2453-2 


2355 
2406 9 
2458-3 


2360 2 
2412 1 
2463 4 


2365-4 
2417-3 
2468-5 


2370-6 
2422-4 
2473-6 


2375-8 
2427-6 
2478-7 


2381-0 
2432-7 
2483-8 


2386 
2437 
2488 


2 
8 
9 


6-2 
5-2 
5-1 



60 



XX. — EXTERIOR BALLISTICS. 



Table III. — Continued. 
Distance and Yelocity Table, Gs = cr^, 



V. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


f.s. 
136 
137 
138 


feet. 
4 2493-9 
2544 4 
2594-3 


feet. 
2499 
2549-4 
2599-2 


feet. 
2504 1 
2554-4 
2604-2 


feet. 
2509-1 
2559-4 
2609 1 


feet. 
2514-2 
2564-4 
2614-1 


feet. 

2519-2 
2569-4 
2619 


feet 
2524- 
2574- 
2624- 


3 

4 



feet. 
2529-3 
2579 4 
2628-9 


feet. 
2534-3 
2584-3 
2633-8 


feet. 
2539-4 
2589-3 
2638-8 


+ 
5 
5 
4 9 


139 
110 
141 


4 2643-7 
2692-6 
2741-2 


2648-6 
2697-5 
2746-0 


2653-5 
2702-4 
2750-8 


2658-4 
2707-2 
2755-7 


2663-3 
2712-1 
2760-5 


2668-2 
2717 
2765-3 


2673 

2721 
2770 


1 
8 
1 


2678-0 
2726-7 
2774-9 


2682-9 
2731-5 
2779-7 


2687-8 
2736-3 
2784-5 


4-9 
4-9 
4-8 


142 
143 
144 


4 2789-3 
2837-1 
2884-4 


2794 1 
2841-8 
2889 1 


2798-9 
2846-6 
2893-8 


2803-7 
2851-3 
2898-6 


2808-5 
2856-0 
2903-3 


2813-2 
2860-8 
2908-0 


2818 
2865 
2912 




5 

7 


2822-8 
2870-2 
2917-4 


2827-5 
2875-0 
2922-1 


2832-3 
2879-7 
2926-7 


4-8 

4-7 
4-7 


145 
146 
147 


4 2931-4 
2978-1 
3024-5 


2936 1 
2982-8 
3029 1 


2940-8 
2987-4 
3033-7 


2945-5 
2992-1 
3038-4 


2950 1 

2996-7 
3043-0 


2954-8 
3001-3 
3047 6 


2959 
3006 
3052 


5 

2 


2964-1 
3010-6 
3056-8 


2968-8 
3015-2 
3061-4 


2973-5 
3019-9 
3066-0 


4 7 
4 6 
4-6 


148 
149 
150 


4 3070-6 
3116 4 
3162-0 


3075-2 
3121 
3166 5 


3079 8 
3125-6 
3171 


3084-4 
3130 1 
3175 6 


3089 
3134-7 
3180 1 


3093-5 
3139-2 
8184-6 


3098 
3143 
3189 


1 
8 
2 


3102-7 
3148-3 
3193-7 


3107-3 
3152-9 
3198-2 


3111-8 
3157-4 
3202-7 


4-6 
4 6 

4-5 


151 
152 
153 


i 3207 2 
3252 3 
3297-2 


3211 • 8 
3256-8 
3301-7 


3216-3 
3261-3 
3306-2 


3220-8 
3265-8 
3310-6 


3225-3 
3270-3 
3315 1 


3229-8 
3274-8 
3319-6 


3234 
3279 
3324 


3 
3 
1 


3238-8 
3283-8 
3328-5 


3243-3 
3288-3 
3333-0 


3247-8 
3292-8 
3337-5 


4-5 
4 5 
4 5 


154 
155 
156 


4 3342-0 
3386-5 
3430 9 


3346-4 
3391-0 
3435-3 


3350 9 
3395-4 
3439-8 


3355-3 
3399-9 
3444-2 


3359-8 
3404 3 
3448-6 


3364-3 
3408-7 
3453 


3368 
3413 
3457 


7 
2 
4 


3373-2 
3417-6 
3461-9 


3377 6 
3422 
3466-3 


3382-1 
3426-5 
3470-7 


4-5 

4-4 
4-4 


157 
158 
159 


4 3475-1 
3519-1 
3563-0 


3479-5 
3523-5 
3567-3 


3483-9 
3527-9 
3571-7 


3488-3 
3532 3 
3576-1 


3492-7 
3536-7 
3580-4 


3497 1 
3541 1 
3584-8 


3501 
3545 
3589 


5 
4 
1 


3505-9 
3549-8 
3593-5 


3510 3 
3554 2 
3597-9 


3514-7 
3558-6 
3602 2 


4-4 
4-4 
4-4 


160 

161 
162 


4 3606 6 
3650-0 
3693-3 


3610-9 
3654-3 
3697 6 


3615-3 
3G58-7 
3701-9 


3619-6 
3663 
3706-1 


3624-0 
3667-3 
3710-5 


3628-3 
3671-6 
3714 8 


3632 
3676 
3719 


6 


1 


3637 
3680-3 
3723-4 


3641-3 
3684-6 
3727-7 


3645-7 
3688-9 
3732-0 


4-3 
4-3 
4-3 


163 
164 
165 


4 3736-3 
3779-2 
3821-9 


3740-6 
3783-5 
3826-2 


3744-9 
3787-8 
3830-4 


3749 2 
3792 
3834-7 


3753-5 
3796-3 
3838-9 


3757-8 
3800-6 
3843-2 


3762 
3804 
3847 


1 
9 
4 


3766-4 
3809-1 
3851-7 


3770 6 
3813-4 
3855-9 


3774-9 
3817-6 
3860-2 


4 3 
4-3 
4-3 


166 
167 
168 


4 3864-4 
3906-8 
3949 


3868-7 
3911-0 
3953 2 


3872-9 
3915-2 
3957-4 


3877-2 
3919-5 
3961-6 


3881-4 
3923-7 
3965-8 


3885-6 
3927-9 
3970-0 


3889 
3932 
3974 


9 
1 
2 


3894-1 
3936 3 

3978-4 


3898-3 
3940 5 
3982-6 


3902-5 
3944-7 
3986-7 


4-2 
4-2 
4 2 


169 

170 
171 


4 3990-9 
4032-7 
407i 3 


3995-1 
4036 9 
4078-5 


3999 3 
40111 
4082-6 


4003-5 
4045-2 
4086-8 


4007-7 
4049-4 
4090-9 


4011-9 
4053-6 
4095-1 


4016 
4057 
4099 



7 
2 


4020-2 
4061-9 
4103 3 


4024-4 
4066-0 
4107-5 


4028-6 
4070-2 
4111-6 


4-2 
4 2 
4 1 


172 
173 
174 


4 4115-7 
4157 
4198 


4119-9 
4161-1 
4202 1 


4124-0 
4165-2 
4206-2 


4128-1 
4169-3 
4210 3 


4132-3 

4173-4 
4214-4 


4136-4 

4177-5 
4218-5 


4140 

4181 
4222 


5 
6 
6 


4144-6 

4185-7 
4226-7 


4148-7 
4189-8 
4230-8 


4152-9 
4193-9 
4234-8 


4-1 
4 1 
4 1 


175 
176 

177 


4 4238 9 
4279 6 
4320 2 


4243 
4283-7 
4324-2 


4247-1 
4287-8 
4328-3 


4251-2 
4291-8 
4332 -3 


4255-3 
4295-9 
4336-4 


4259-3 
4300-0 
4340-4 


4263 
4304 
4344 


-4 

-4 


4267-5 
4308-8 
4348 5 


4271-5 
4312-1 
4352-5 


4275-6 
4316 1 
4356-5 


4-1 
41 
4-0 


178 
179 
180 


4 4360-5 
4100 7 
4440-8 


4364-6 
4404-7 
4444-7 


4368-6 
4408 8 
4448-7 


4372-0 
4412-8 
4452-7 


4376-6 
4416 8 
4456-7 


4380-7 
4420-8 
4460-7 


4384 
4424 
4464 


-7 
-8 
7 


4388-7 
4428-8 
4468-7 


4392 7 
4432 8 
4472-6 


4396-7 
4436-8 
4476-6 


40 
4 
40 


181 
182 
183 


4 4480 6 
4520-3 
4559-8 


4484-6 
4524-2 
4563-7 


4488 5 
4528-2 
4567-7 


4492 5 
4532-2 
4571-6 


4496-5 
4536 1 
4575-6 


4500 5 
4540-1 
4579-5 


4501 
4544 
4583 


•4 

4 


4. '08 -4 
4518 
4587-4 


4512-4 
4551-9 
4591-3 


4516-3 
4555 9 
4595-2 


4-0 
40 
3-9 



XX. — EXTERIOR BALLISTICS. 



61 



Table III . — Continued. 
Distance and Velocity Table, Cs — a^' — cr^„. 



V. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diffi 


f.s. 

184 
185 ! 
186 


feet. 

4 4599-2 
4638-4 
4677-4 


feet. 
4603-1 
4642-3 
4681-3 


feel 
4607 
4646 
4685 




2 
2 


feet 
4610 
4650 
4689 


9 


feet. 
4614-9 
4654 
4693-0 


feel 

4618 
4657 
4696 


8 
9 
9 


feet. 

4622-7 
4661-8 
4700 8 


feel 

4626 
4665 
4704 


6 

7 
6 


feet. 

4630-5 
4669-6 
4708-5 


feet. 
4634-4 
4673 5 
4712-4 


+ 
3-9 
3-9 
3-9 


187 
188 ' 
189 


4 4716 3 
4755 
4793 7 


4720-2 
4758-9 
4797-5 


4724 
4762 
4801 


1 

8 
4 


4727 
4766 
4805 




4731-8 
4770 5 
4809-1 


4735 

4774 
4812 


7 
4 
9 


4739-6 
4778-2 
4816-8 


4743 
4782 
4820 


4 

1 
6 


4747-3 
4786-0 
4824-5 


4751-2 
4789-8 
4828-3 


3 9 
3 9 
3 8 


190 

191 i 

192 j 


4 4832-2 
4870-5 
4908-7 


4836 

4874-3 
4912 5 


4839 
4878 
4916 


8 
1 
3 


4843 

4882 
4920 




4847-5 
4885-8 
4923-9 


4861 
4889 
4927 


4 
6 

7 


4855-2 
4893 4 
4931-5 


4859 
4897 
4935 



3 
3 


4862-8 
4901-1 
4939-1 


4866-7 
4904-9 
4942-9 


3 8 
3 8 
3 8 


193 i 

194 

195 


4 4946-7 
4984-5 
5022 2 


4950-5 
4988-3 
5025 9 


4954 
4992 
5029 


3 

1 
7 


4958 
4995 
5033 




4961-9 
4999 6 
6037-2 


4965 
5003 
5040 


7 
4 
9 


4969-4 
5007-1 
5044-7 


4973 
5010 

5048 


2 
9 
4 


4977-0 
5014 7 
5052-1 


4980-7 
5018-4 
5055-9 


3-8 
3-8 
3 7 


196 
197 

198 , 


4 5059-6 
5096-9 
5133-9 


5063-4 
5100 6 
6137-5 


5067 
5104 
6141 


1 
3 
2 


5070 
5108 
5144 


8 

9 


5074-6 
5111-7 
5148 6 


5078 
5115 
5152 


3 

4 
3 


5082-0 
5119 1 
5150-0 


5085 
5122 
5159 


7 
8 
6 


6089-4 
5126-5 
5163-3 


5093 1 
5130 2 
6166 9 


3-7 
3-7 
3 7 


199 
200 
201 


4 5170-6 
5207-1 
5243-3 


5174-3 
5210-7 
6246-9 


5177 
5214 
5250 


9 
3 
5 


5181 
5218 
5254 


6 


1 


5185-2 
5221-6 

5257-7 


5188 
5225 
5261 


9 
2 
3 


5192-5 
5228-8 
6264-9 


5196 
5232 
5268 


2 
5 
5 


5199-8 
5236-1 
5272-1 


5203-4 
5239-7 
5275 7 


3 6 

3 6 
3 6 


202 

203 
204 


4 5279 2 
631 i 9 
6360-3 


5282 8 
6318-5 
5353-8 


5286 
5322 
5357 


4 

3 


5290 
5325 
5360 



6 
9 


5293-0 
5329-1 
6364-4 


5297 
5332 
5367 


2 

7 
9 


5300-7 
5336 2 
6371-4 


5304 
5339 
5374 


3 

7 
9 


5307-8 
5343-3 
5378-4 


5311 4 
5346 8 
5391 9 


3 6 
3 5 
3-5 


205 
206 
207 


4 5385-4 
6420-2 
5454-7 


5388 9 
5423-7 
6458-1 


5392 
5427 
5461 


4 

1 
6 


5395 
5430 
5465 


9 
6 



5399-4 
5434-1 
6468-4 


5402 

5437 
5471 


9 
5 
9 


5406-3 
5441 
5475-3 


5409 
5444 
5478 


8 
4 

7 


5413-3 
5447-8 
5482-1 


5416-7 
5451-3 
5485-6 


3 5 
3 5 
3 4 


208 

209 ! 

210 ' 


4 5488-9 
5522-8 
5556 4 


5492-3 
5526 2 
5559-8 


6495 
5529 
6563 


7 
6 
1 


5499 
5532 
6566 


1 
9 
4 


5502-5 
5536-3 
5569 8 


5505 
5539 
6573 


9 

7 
1 


5509 3 
5543 
6576 5 


5512 
5546 
5579 


7 
4 
8 


5516-1 
5549-7 
5583-1 


6519-4 
5553-1 
6586-4 


3 4 
3 4 
3-3 


211 
212 
213 


4 5589-7 
6622-8 
5655-5 


5593 
6626-1 
6658-8 


5596 
5029 
5662 


4 

3 



5599 
5632 
5665 


7 
6 
3 


5603-0 
5635-9 
5668-6 


5606 
5639 
5671 


3 

2 
8 


5609-6 
5642-5 
6675 - 1 


5612 
5645 
5678 


9 

7 
3 


5616-2 
5649-0 
5681-5 


5619-5 
5652-3 
5684-8 


3 3 
3-3 
3-2 


214 ' 

215 ! 
216 


4 5688 
6/20-2 
6752-2 


5691 2 
5723-4 
5755-4 


5694 

5726 
5758 


5 
6 
6 


5697 
5729 
5761 


7 
9 
8 


5700-9 
5733-1 
6764 9 


5704 
5736 
5768 


2 
3 

1 


5707-4 
5739-5 
6771-3 


5710 

5742 

5774 


6 

6 
4 


5713-8 
5745-8 
5777-6 


5717-0 
6749-0 
6780 8 


3 2 
3 2 
3 2 


217 ' 

218 

219 


4 5783 9 
5815-4 
5846 6 


5787-1 
5818-5 
5849 7 


6790 
5821 
6852 


2 
6 
8 


5793 
5824 
5855 


4 
8 
9 


5796-6 
5827-9 
5859 


5799 
5831 
5862 


7 

1 


5802-9 
6834 1 
5865-2 


5806 
5837 
5868 



3 
3 


5809-1 
5840-4 
5871-4 


5812-2 
6843 5 
5874-4 


3 1 
3 1 
3 1 


220 
221 
222 


4 5877-5 
5908 3 
5938-7 


5880-6 
5911 3 
5941-8 


«883 
5914 
6944 


7 
4 
8 


5886 
5917 
5947 


8 
4 
8 


6889-9 
5920-5 
5950-9 


5893 
6923 
5963 



6 
9 


5896-0 
5926-6 
5956-9 


5899 
5929 
5959 


1 
6 
9 


5902-1 
5932-7 
6963-0 


5905 2 
5935-7 
5966-0 


3 1 
3 
3 


223 
224 : 
225 


4 5969-0 
5999 
6028 7 


5972-0 
6002 
6031 7 


5975 
6004 
6034 




9 
6 


6978 
6007 
6037 



9 
6 


5981 
6010 9 
6040-5 


5984 
6013 
6043 




9 
5 


5987-0 
6016 9 
6046 5 


5990 
6019 
6049 




8 
4 


5993-0 
60-22 8 
6052 4 


5996-0 
6025-8 1 
6055 3 j 

6084 7 ' 

6113-8 

6142-8 


30 
3 
3 


226 

227 j 

228 


4 0058-3 
6087-6 
6116-7 


6061-2 
6090 5 
6119 6 


6064 
6093 
6122 


1 
4 
5 


0067-1 
C0'.)6 3 
6125 4 


0070-0 
6099-3 
6128 3 


6072 
6102 
6131 


9 
2 

-2 


6075-9 
6105 1 
6134 1 


6078 
6108 
6137 


8 




6081-7 
6110 9 
0139-9 


2 9 
2 9 
29 


2^-0 ^ 


4 6145 -7 
6174-6 


6148-6 
6177-5 


6151 5 
6180-4 


6154-4 
6183-3 


6157 3 
6186-2 


6160 
6189 


1 

4 


6163 1 
6191-9 


6166 
6194 




8 


6168 8 
6197-7 


6171 7 
6200-6 


2-9 
2 9 





62 



XX. — EXTERIOR BALLISTICS. 



Table IV.* 
Inclination and Velocity Table, Cd — d^, — S^„. 



V. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


f.8. 

40 
41 
42 


d( 

4 
9 


?g8. 


6757 
0056 


Cl( 

5 
9 


3g8. 
4838 
1240 
4207 


d 

5 
9 


9640 
5688 
8327 


d( 

1 

6 

10 


4407 
0101 
2410 


d( 

1 

6 

10 


3ff8. 
9137 
4482 
6467 


d 

2 

6 

11 


3^8. 
3830 
8828 
0496 


d 

2 

7 

11 


3S8. 
8488 
3141 
4494 


d 

3 

7 

11 


3110 

7421 
8462 


d 

8 
12 


3^8. 
7689 
1660 
2397 


degs. 

4-2240 

8-5874 

12-6306 


43 


13 
16 
20 


0187 
7450 
2125 


13 
17 
20 


4039 
1030 
5460 


13 
17 
20 


7862 
4585 
8772 


14 
17 
21 


1652 
8110 
2054 


14 
18 
21 


5419 
1614 
5320 


14 
18 
21 


9159 

5094 
8565 


15 

18 
22 


2872 
8549 
1788 


15 
19 
22 


6557 
1980 
4989 


16 
19 
22 


0211 
5383 
8169 


16-3843 
19.8766 
23 1327 


46 
47 

48 


23 
26 
29 


4463 
4691 
3006 


23 
26 
29 


7578 
7607 
5739 


24 
27 
29 


0671 
0503 
8455 


24 

27 
30 


3736 
3376 
1151 


24 

27 
30 


6788 
6234 
3833 


24 
27 
30 


9821 
9075 
6498 


25 
28 
30 


2C34 
1897 
9147 


25 
28 
31 


5927 
4702 
1779 


25 
28 
31 


8801 
7486 
4393 


26 1756 
29-0254 
31-6993 


49 
60 

ei 


31 
34 
36 


9576 

4557 
8073 


32 
34 
37 


2143 
6973 
0349 


32 
34 
37 


4695 
9375 
2613 


32 
35 
37 


7227 
1761 
4862 


32 
35 
37 


9747 
4134 
7099 


33 

35 
37 


2253 
6493 
9323 


33 

35 
38 


4743 
8837 
1534 


33 
36 
38 


7219 
1167 
3731 


33 

36 
38 


9679 
3480 
5914 


34 2125 
36-5783 
38-8086 


52 
53 

54 


39 
41 
43 


0246 
1175 
0967 


39 
41 
43 


2394 
3204 

2887 


39 
41 
43 


4529 
5221 
4795 


39 
41 
43 


6651 
7225 
6690 


39 
41 
43 


8762 
9221 
8578 


40 

42 
44 


0860 
1205 
0456 


40 

42 
44 


2947 
3179 
2324 


40 
42 
44 


5022 
5142 
4182 


40 
42 
44 


7083 
7095 
6031 


40-9135 
42-9037 

44-7870 


55 
56 
57 


44 
46 
48 


9698 
7437 
4270 


45 
46 
48 


1510 
9160 
5906 


45 

47 
48 


3325 
0874 
7534 


45 

47 
48 


5122 
2581 
9153 


45 
47 
49 


6910 
4277 
0764 


45 
47 
49 


8689 
5965 
2368 


46 

47 
49 


0457 
7644 
3963 


46 

47 
49 


2217 
9314 
5551 


46 
48 
49 


3964 
0973 
7130 


46-5705 
48-2625 
49-8701 


58 
59 
60 


50 
51 
53 


0265 
5492 
0003 


50 
51 
53 


1822 
6975 
1417 


50 
51 
53 


3370 

8451 
2825 


50 
51 
53 


4909 
9917 
4224 


50 
52 
53 


6442 

1378 
5618 


50 
52 
53 


7968 
2832 
7005 


50 
52 
53 


9487 
4280 
8386 


51 
52 
53 


0999 
5721 
9761 


51 
52 
54 


2505 
7155 
1130 


51-4002 

52-8583 
54-2492 


61 
62 
63 


54 
55 
56 


3847 
7054 
9663 


54 
55 

57 


5196 
8342 
0891 


54 
55 
57 


6539 
9623 
2114 


54 
56 

57 


7875 
0899 
3330 


54 
56 
57 


9205 
2169 
4542 


55 
56 

57 


0529 
3433 
5749 


55 
56 
57 


1846 
4690 
6950 


55 
56 

57 


3158 
5942 
8146 


55 
56 

57 


4462 
7188 
9338 


55-5761 
56-8428 
58-0523 


64 
65 

66 


58 
59 
60 


1703 
3209 
4207 


58 
59 
60 


2878 
4332 
5280 


58 
59 
60 


4046 
5449 
6348 


58 
59 
60 


5209 
6562 
7411 


58 
59 
60 


6367 
7669 
8470 


58 
59 
60 


7521 
8772 
9523 


58 
59 
61 


8669 
9869 
0572 


58 
60 
61 


9832 
0961 
1616 


59 
60 
61 


0949 
2047 
2654 


59-2081 
60 3130 
61-3688 


67 
68 
69 


61 
62 
63 


4719 
4779 
4414 


61 

62 
63 


5744 
5761 
5356 


61 
62 
63 


6766 
6739 
6294 


61 
62 
63 


7783 
7711 

7227 


61 
62 
63 


8796 
8680 
8157 


61 
62 
63 


9804 
9646 
9084 


62 
63 
64 


0808 
0607 
0006 


62 
63 

64 


1807 
1565 
0924 


62 
63 
64 


2802 
2519 
1838 


62 3793 
63-3468 
64 2749 


70 
71 

72 


64 
65 
66 


3656 
2522 
1015 


64 
65 
66 


4559 
3388 
1845 


64 
65 
66 


5459 
4250 
2671 


64 
65 
66 


6356 
5107 
3494 


64 
65 
66 


7249 
5962 
4313 


64 
65 
66 


8137 
6813 
5128 


64 
65 
66 


9022 
7660 
5940 


64 
65 
66 


9903 
8504 
6749 


65 
65 
66 


0779 
9345 
7553 


65-1652 
66-0182 
66-8355 


73 
74 
75 


66 
67 
68 


9153 
6955 
4436 


66 

67 
68 


9949 
7717 
5168 


67 
67 
68 


0740 
8476 
5896 


67 
67 
68 


1529 
9231 
6620 


67 
67 
68 


2314 
9983 
7342 


67 
68 
68 


3096 
0733 
8062 


67 
68 
68 


3875 
1479 
8778 


67 
68 
68 


4649 
2223 
9492 


67 
68 
69 


5422 
2964 
0204 


67-6190 
68-3702 
69 0912 


76 

77 
78 


69 
69 
70 


1617 
8497 
5082 


69 
69 
70 


2318 
9169 
5725 


69 
69 
70 


3017 
9838 
6365 


69 
70 
70 


3712 
0503 
7004 


69 
70 
70 


4404 
1166 
7639 


69 
70 
70 


5094 
1826 
8271 


69 
70 
70 


5780 
2483 
8901 


69 
70 
70 


6464 
3137 
9527 


69 
70 
71 


7145 
3787 
0149 


69-7823 
70-4436 
71-0770 


79 
80 
81 


71 
71 
72 


1388 
7432 
3225 


71 
71 

72 


2004 
8023 
3791 


71 
71 

72 


2617 
8611 
4354 


71 

71 

72 


3228 
9196 
4915 


71 
71 

72 


3837 
9779 
5473 


71 

72 
72 


4442 
0359 
6030 


71 

72 
72 


5045 
0937 
6584 


71 

72 
72 


5646 
1513 
7135 


71 

72 
72 


6244 
2086 
7685 


71-6839 
72 2656 
72-8232 


82 
83 

84 


72 
73 
73 


8776 
4079 
9143 


72 
73 
73 


9317 
4596 
9636 


72 
73 
74 


9856 
5111 
0127 


73 

73 
74 


0393 

5622 
0615 


73 
73 

74 


0927 
6132 
1101 


73 
73 
74 


1458 
6639 
1585 


73 
73 

74 


1988 
7145 
2067 


73 
73 

74 


2514 
7648 
2546 


73 

73 

74 


3038 
8149 
3023 


73-3560 
73-8647 
74-3498 


85 
86 
87 


74 
74 
75 


3971 
8573 
2966 


74 
74 
75 


4441 
9022 
3395 


74 
74 
75 


4910 
9468 
3821 


74 
74 
75 


5376 
9912 
4246 


74 
75 
75 


5839 
0355 
4668 


74 
75 
75 


6301 
0795 
5089 


74 
75 
75 


6760 
1233 
5507 


74 
75 
75 


7217 
1669 
5924 


74 
75 
75 


7670 
2104 
6339 


74-8123 
75-2536 
75-6752 



By W. D. Kiven, Esq., M. A., F. S. S. 



XX. EXTERIOR BALLISTICS. 



Table lY .—Continued. 
Inclination and Velocity Table, Cd = 8^ — S^„ 



V. 





1 


!3 


3 


4 


5 


6 


7 


8 


9 


f.8. 

88 

89 1 
90 


degs. 

75 7163 

76 1171 
76-5005 


degs. 
75-7572 
76-1562 
76-5379 


degs. 
75-7980 
76-1952 
76-5751 


degs. 

75 8385 
76-2339 

76 6121 


degs. 

75-8788 
76-2725 
76-6490 


degs. 

75-9190 

i 76-3109 

76-6857 


degs. 
75 9590 
76-3492 
76-7223 


degs. 
75-9988 
76-3873 
76-7588 


d 

76 
76 
76 


4252 
7951 


degs. 
76-0778 
76-4629 
76 8312 


91 
92 
93 


76-8671 
77-2179 
77-5540 


76-9029 
77-2522 
77-5868 


76-9385 
77-2863 
77-6195 


76-9739 
77-3203 
77-6520 


77-0092 
77-3541 
77-6844 


77-0444 

77-3878 
77-7167 


77 0794 
77 4213 

77-7488 


77-1142 

77-4547 
77-7807 


77 
77 
77 


1489 
4879 
81-25 


77-1835 
77-5210 
77 8442 


94 

95 
96 


77-8757 
78 1841 
78-4798 


77 9071 
78-2142 

78 5087 


77-9384 
78-2442 
78-5375 


77-9695 
78-2741 
78-5622 


78-0005 
78 3039 
78-5947 


78-0314 
78-3335 
78-6231 


78 0622 
78-3630 
78-6514 


78-0929 
78-3924 
78-6796 


78 
78 
78 


1234 
4216 
7076 


78 1538 
78 4508 
78 7356 


97 
98 
99 


78-7634 
79-0354 
79-2968 


78-7911 
79 0621 
79-3224 


78-8188 
79-0886 
79-3478 


78 8463 

79 1150 
79-3731 


78-8736 
79 1413 
79-3983 


78-9009 
79 1675 
79-4234 


78-9280 
79 1936 
79-4484 


78-9551 
79-2195 
79-4734 


78 
79 
79 


9819 
2454 
4982 


79-0087 
79-2712 
79 5230 


100 
101 1 
102 


79-5476 
79-7889 
80-0203 


79-5722 
79-8124 
80 0430 


79-5966 
79-8359 
80-0655 


79-6210 
79-8593 
80-0879 


79-6453 
79-8826 
80 1102 


79 6695 
79-9058 

80 1324 


79-6935 
79 9289 
80-1544 


79-7175 
79-9519 
80-1763 


79 
79 
80 


7414 
9748 
1981 


79 7652 
79-9976 
80-2197 


103 
104 

105 


80-2412 
80-4466 
80-6321 


80-2625 
80-4661 
80-6495 


80-2837 
80-4854 
80-6667 


80-3408 
80-5045 
80-6835 


80-3256 
80 5234 
80 7003 


80-3462 
80 5420 
80 7169 


80 3667 
80 5605 
80 7333 


80-3869 
80-5787 
80-7495 


80 
80 
80 


4071 

5967 
7654 


80-4270 
80 6145 
80 7813 


106 

107 ' 

108 1 


80 7970 
80-9463 
81-0841 


80-8126 
80-9606 
81-0973 


80-8280 
80-9747 
81 1105 


80-8432 
80-9886 
81 1236 


80-8583 
81 0026 
81 1366 


80-8733 

I 81 0164 

81 1495 


80-8882 
81-0301 
81 1624 


80 9029 

81 0437 
81 1751 


80 
81 
81 


9175 
0573 
1877 


80-?319 
81 0707 
81 2003 


109 
110 
lllj 


81-2129 
81-3342 
81-4495 


81-2253 
81-3460 
81-4607 


81-2377 
81-3578 
81-4719 


81 2501 
81 3695 
81 4829 


81-2623 
81-3811 
81 4939 


81-2745 
81-3927 
81 5049 


81-2866 
81-4042 
81-5159 


81-2986 
81-4156 
81-5268 


81 
81 
81 


3105 
4269 
5377 


81-3224 
81 4382 
81 5486 


112 
113 
114 ! 


81-5593 
81-6647 
81 7662 


81-5700 
81-6750 
81-7761 


81-5807 
81-6853 
81-7861 


81-5913 
81-6955 
81-7960 


81-6019 
81-7057 
81-8058 


81-6124 
81 7159 
81-8156 


81-6230 
81-7260 
81-8254 


81-6334 
81-7361 
81-8351 


81 
81 
81 


6439 

7462 
8448 


81-6543 
81-7662 
81 •8545 


115 
116 
117 


81-8641 
81-9588 
82-0503 


81-8737 
81-9681 
82-0592 


81-8833 
81-9774 
82-0682 


81-8929 
81-9866 
82 0771 


81-9024 
81-9958 
82-0860 


81-9119 
82-0049 
82 0948 


81-9213 
82 0141 
82 1036 


81-9307 
82-0232 
82 1124 


81 
82 
82 


9401 
0322 
1212 


81-9496 
82 0413 
82-1299 


118 
119 
120 


82 1386 
82-2241 
82-3066 


82-1473 
82-2325 
82-3147 


82 1559 
82-2408 
82-3228 


82 1645 
82-2492 
82 3309 


82 1731 
82-2575 
82-3389 


82-1817 
82-2657 
82-3469 


82-1902 
82-2Y40 
82-3549 


82-1988 
82-2822 
82-3629 


82 
82 
82 


2073 
2903 
3708 


82-2157 
82-2985 
82-3787 


121 
122 
123 


82-3865 
82-4639 
82 5386 


82-3944 
82-4715 
82-5459 


82-4022 
82-4790 
82 5533 


82-4100 
82-4865 
82-5606 


82-4178 
82-4940 
82-5679 


82-4255 
82 5015 
82-5751 


82-4333 
82-5090 
82-5824 


82-4410 
82-5164 
82-5896 


82 
82 
82 


4486 
5238 
5968 


82-4563 
82-5312 
82 6040 


124 
125 
126 


82-6112 
82-6814 
82-7494 


82-6183 
82-6883 
82-7561 


82-6254 
82-6951 
82-7627 


82 6324 
82-7019 
82 7694 


82-6395 
82-7088 
82 7760 


82-6465 
82-7156 
82-7826 


82-6535 

82-7224 
82-7892 


82-6605 
82-7291 
82-7957 


82 

82 
82 


6675 
7359 
8023 


82-6744 
82-7427 
82-8088 


127 
128 
129 


82-8153 
82-8794 
82-9415 


82-8218 
82-8857 
82-9477 


82-8283 
82-8920 
82-9538 


82-8348 
82-8983 
82-9599 


82-8412 
82-9045 
82-9660 


82-8477 
82-9107 
82-9720 


82-8541 
82-9169 
82-9780 


82-8604 
82-9231 
82-9840 


82 
82 
82 


8668 
9292 
9900 


82-8731 
82-9354 
82-9900 


130 
131 
132 


83-0019 
83 0606 
83 1176 


83-0079 
83-0664 
83 1232 


83-0138 
83-0721 
83-1288 


83 0197 
83-0779 
83-1344 


83-0256 
83-0836 
83-1400 


83 0315 
83-0893 
83 1455 


83-0373 
83 0950 
83 1511 


83-0432 
83-1007 
83 1566 


83 
83 
83 


0490 
10^3 
1621 


83 0548 
83-1119 
83-1676 


133 
184 
136 


83-1730 
83-2271 
83-2797 


83-1785 
83-2324 
83-2849 


83 1840 
83-2377 
83-2900 


83-1894 
83-2430 
83-2951 


83 1949 
83-2483 
83-3003 


83-2003 
83-2536 
83-3054 


83-2057 
83-2588 
83-3105 


83 2110 
83-2641 
83-3156 


83 
83 
83 


2164 
2693 
3207 


83 2217 
83 2745 
83-3257 



64 



XX. — EXTERIOR BALLISTICS. 



Table lY .—Continued. 
Inclination and Velocity Table, Cd = d^, 



.. 





1 


2 


3 


4 


5 


6 


7 


8 


" 


f.s. 

136 
137 
138 


degs. 
83-3308 
83-3808 
83-4295 


d( 

83 
83 
83 


5gS. 
3359 
3857 
4343 


degs. 
83-3409 
83-3906 
83-4391 


degs. 

83-3459 
83-3955 
83-4438 


d( 

83 
83 
83 


3509 
4004 
4486 


d( 

83 
83 
83 


3560 
4053 
4533 


d< 

83 
83 
83 


3g8. 
3609 
4101 

4581 


d( 

83 
83 

83 


5g8. 
3659 
4150 
4628 


d( 

83 

83 
83 


3g8. 
3709 
4198 
4676 


degs. 
83-3759 
83-4247 
83-4723 


139 
140 ' 
141 


83 
83 
83 


4770 
5233 
5687 


83 
83 
83 


4817 
5279 
5732 


83-4863 
83-5325 
83-5777 


83-4910 
83-5371 
83-5821 


83 
83 
83 


4956 
5417 
5866 


83 
83 
83 


5003 

5402 
5910 


83 
83 
83 


5049 
5507 
5954 


83 
83 
83 


5095 
5553 
5999 


83 
83 
83 


5141 
5598 
6043 


83-5187 
83-5642 
83-6087 


142 
143 
144 


83 
83 
83 


6130 
6565 
6988 


83 
83 
83 


6174 
6607 
7030 


83-6218 
83 - 0650 
83-7072 


83-6261 
83-6693 
83-7114 


83 
83 
83 


6305 
6735 
7156 


83 
83 
83 


6348 
6778 
7197 


83 
83 
83 


6392 
6820 
7239 


83 
83 
83 


6435 

6862 
7280 


83 
83 
83 


6478 
6904 
7321 


83-6522 
83-6946 
83-7362 


145 \ 

146 i 
147 


83 
83 
83 


7403 
7810 
8209 


83 
83 
83 


7444 
7850 
8249 


83-7485 
8.3-7891 
83-8-288 


83-7526 
83-7930 
83 8327 


83 
83 


7567 
7970 
8366 


83 
83 
83 


7608 
8010 
8406 


83 

83 
83 


7649 
8050 
8445 


83 
83 
83 


7689 
8090 
8484 


83 
83 
83 


7730 
8130 
8522 


83-7770 
83 '8170 
83-8561 


148 
149 
150 


83 
83 
83 


8600 
8983 
9359 


83 
83 
83 


8639 
9021 
9396 


83-8677 
83-9059 
83-9433 


83-8715 
83 9096 
83-9470 


83 
83 

83 


8754 
9134 
9507 


83 
83 
83 


8792 
9172 
9544 


83 
83 
83 


8830 
9209 
9581 


83 
83 
83 


8869 
9247 
9617 


83 
83 
83 


8907 
9285 
9654 


83-8945 
83-9322 
83-9691 


151 ' 

152 

153 


83 
84 
84 


9727 
0090 
0446 


83 
84 
84 


9764 
0126 
0481 


83-9800 
84-0161 
84-0516 


83-9837 
84-0197 
84-0551 


83 
84 
84 


9873 
0233 
0587 


83 
84 
84 


9909 
0269 
0622 


83 
84 
84 


9946 
0304 

0657 


83 
84 
84 


9982 
0340 
0692 


84 
84 
84 


0018 
0375 
0727 


84-0054 
84-0410 
84-0762 


15. 
155 

156 


84 
84 
84 


0796 
1140 
1479 


84 
84 
84 


0831 
1174 
1513 


84-0866 
84 1208 
84-1546 


84-0900 
84-1242 
84-1579 


84 
84 
84 


0935 
1276 
1613 


84 
84 

84 


0969 
1310 
1646 


84 
84 
84 


1004 
1344 
1679 


84 
84 
84 


1038 
1378 
1713 


84 
84 
84 


1072 
1412 
1746 


84-1106 
84 1445 
84-1779 


157 
158 
159 


84 
84 
84 


1812 
2139 
2461 


84 
84 
84 


1845 
2172 
2493 


84-1878 
84-2204 
84-2525 


84-1911 
84-2237 
84-2557 


84 
84 
84 


1943 
2269 
2588 


84 
84 
84 


1976 
2301 
2620 


84 
84 
84 


2009 
2333 
2652 


84 
84 
84 


2041 
2366 
2683 


84 
84 
84 


2074 
2398 
2715 


84-2107 
84-2430 
84-2746 


160 ' 

161 

162 


84 
84 
84 


2778 
3088 
3394 


84 
84 
84 


2809 
3119 
3424 


84-2840 
84-3150 
84-3454 


84-2871 
84-3180 
84-3484 


84 
84 
84 


2902 
3210 
3514 


84 

84 

,84 


2933 
3242 
3544 


84 

84 
84 


2965 
3272 
3574 


84 
84 

84 


2996 
3302 
3604 


84 
81 
84 


3027 
3333 
3634 


84-3058 
84-3363 
84-3664 


163 
164 
165 


84 
84 
84 


3694 
3990 
4281 


84 
84 
84 


3724 
4019 
4310 


84-3753 
84-4018 
84-4339 


84-3783 
84-4078 
84-4367 


84 
84 
84 


3813 
4107 
4396 


84 
81 
84 


3843 

41S6 
4425 


84 
84 
84 


3872 
4105 
4453 


84 
84 
84 


3902 
4194 

4482 


84 
84 
84 


3931 
4223 
4510 


84-3960 
84-4252 
84-4539 


166 
137 
168 


84 
84 
84 


4567 
4849 
5127 


84 
84 
84 


4595 
4877 
5154 


84-4624 
84-4905 
84-5181 


84-4652 
84-4933 
84-5209 


84 
84 
84 


4680 
4961 
5236 


84 
84 
84 


4709 
4988 
5263 


84 
84 
84 


4737 
5016 
5291 


84 
84 
84 


4765 
5044 
5318 


84 
84 
84 


4793 
5070 
5345 


84-4821 
84-5099 
84-5372 


169 
170 
171 


84 
84 
84 


5399 
5668 
5933 


84 
84 
84 


5426 
5695 
5959 


84-5453 
84-5721 
84-5985 


84-5480 
84-5748 
84-6012 


84 
84 
84 


5508 

5775 
6038 


84 
84 
84 


5534 
6801 
6064 


84 
84 
84 


5561 
5828 
6090 


84 
84 
84 


5588 
5854 
6116 


84 

84 
84 


5615 
5880 
6142 


84-5641 
84-5907 
84 0168 


172 
173 
174 


84 
84 

84 


6193 
6449 
6701 


84 
84 
84 


6219 
6475 
6726 


84-6245 
84-6500 
84-6750 


84-6271 
84-6525 
84-6776 


84 
84 
84 


6297 
6550 
6800 


84 
84 
84 


6322 
6575 
6825 


84 
84 
84 


6348 
6001 
6850 


84 

84 
84 


6373 
6626 
6875 


84 
84 
84 


6399 
6651 
6899 


84-6424 
84-6676 
84-6924 


175 
176 

177 


84 
84 
84 


6948 
7192 
7432 


84 
84 
84 


6973 
7216 
7455 


84-6997 
84-7240 
84-7479 


84-7022 
84-7264 
84-7503 


84 
84 
84 


7046 
7288 
7526 


84 
84 
84 


7071 
7312 
7550 


84 
84 
84 


7095 
7336 
7574 


84 
84 
84 


7119 
7360 
7597 


84 
84 
84 


7144 
7384 
7621 


84-7168 
84-7408 
84-7645 


178 
179 
180 


81 
84 
84 


7608 
7P02 
8131 


84 
81 
84 


7692 
•7925 
8154 


81 -771 5 
84-7918 
84-8177 


84-7739 
81-7972 
8i-8199 


84 

81 
84 


7762. 
7904 
8222 


•84 
81 
81 


7785 

roi7 

8214 


84 
84 
84 


7809 

80 :o 

82u7 


84 
84 
84 


7832 
803 
8289 


84 
84 
84 


7855 
80SG 
8312 


84-7878 
81-8109 
84-8334 


181 

182 
183 


84 
84 
84 


83R7 
8579 
8798 


81 

84 
84 


8379 
8601 
8819 


84-8-101 
84-8623 
84-8841 


81 ■ 8424 
84-8645 
84-8863 


84 
84 

84 


8446 
8667 
8884 


84 
i ^* 


8168 
8689 
8906 


84 
84 

84 


81 PO 

8711 
8927 


84 
84 
84 


8513 

8732 
8949 


84 
84 
84 


8535 
8754 
8970 


84-8557 
84-8776 
84-8992 



XX. — EXTERIOR BALLIStlCS. 



Table IV.— Continued. 
Inclination and Velocity Table, Cd = S^, — S^„. 



V. 





1 


2 


3 


4 


5 


6 


7 


8 





f.s. 

184 
185 
186 


d 

84 
84 
84 


9013 
9226 
9435 


d 

84 
84 
84 


egs. 
9035 
9247 
9456 


d 

84 
84 
84 


9056 
9268 

9476 


d 
84 
84 
84 


egs. 

9077 
•9289 

9497 


d 

84 
84 
84 


egs. 
•9099 
•9310 
9518 


d 

84 
34 
84 


9120 
9331 
•9538 


d 

84 
84 
84 


egs. 
9141 
9351 

•9559 


degs. 
84-9162 
84 9372 
84-9580 


d 

84 
84 
84 


egs. 
■9184 
■9393 
-9600 


degs. 

84-9205 
84 9414 
84-9621 


1?7 
188 
189 


84 
84 
85 


9C41 
•9845 
0045 


84 
84 
86 


9C62 
9865 
0065 


84 
84 
85 


9682 
9885 
0085 


84 
84 
85 


9702 
9905 
0105 


84 
84 
85 


9723 
9925 
0125 


84 
84 
85 


•9743 
•9946 
•0145 


84 
84 
85 


9763 
•9966 
0165 


84 • 9784 
84-9986 
85 0185 


84 
85 
85 


9804 
0006 
0204 


84-9820 
86-0026 
85-0224 


190 
191 
192 


85 

85 
85 


0244 
0438 
0630 


85 
85 
85 


0263 
0458 
0650 


85 
85 
85 


0283 
0477 
0669 


85 
85 
85 


0303 
0496 
0687 


85 
85 
85 


0322 
0515 
0706 


85 
85 
85 


0342 
0535 
0725 


85 
85 
85 


•0361 
0554 
0744 


85 0380 

86 0573 
85 0763 


85 
85 
85 


0400 
0592 
0782 


8.'5 0419 
85-0611 
85-0801 


193 
194 
195 


85 
85 
85 


0820 
1006 
1190 


85 
85 

85 


0838 
1025 
1208 


85 
85 
85 


0857 
1043 
1227 


86 
86 
85 


0876 
10C2 
1245 


85 
85 
85 


0895 
1080 
1263 


85 
85 
85 


0913 
1099 
1281 


85 
85 
85 


•0932 
1117 
1299 


85 0951 
85 1136 
85 1317 


85 
85 
85 


0969 
1154 
1335 


85-0988 
86 1172 
85 -136a 


196 
197 
198 


85 
85 
85 


1371 
1549 
1724 


85 
86 
85 


1389 
1567 
1741 


85 
85 

85 


1407 
1584 
1759 


85 
85 
85 


1425 
1602 
1776 


85 
85 
85 


1443 
1619 
1793 


85 
85 
85 


1460 
1637 
1810 


85 
85 
85 


1478 
1654 

1827 


85 1496 
85-1672 

85 1844 


85 
85 
85 


1514 
1689 
1862 


86-1531 
85 1707 
86-1879 


199 
200 
201 


85 
85 
85 


1896 
2065 
2231 


85 
85 
85 


1913 
2081 
2247 


85 
85 
85 


1930 ' 

2098 

2264 


86 
85 
85 


1947 
2115 
2280 


85 
85 
85 


1964 
2131 
2290 


84 
85 
85 


1981 
2148 
2313 


85 
85 
85 


1998 
2165 
2329 


85 2014 
85-2181 
85-2346 


85 
85 
85 


2031 
2198 
2362 


86-2043 
85-2214 
85-2378 


202 
203 
204 


85 
85 
85 


2394 

2556* 

2714 


85 
85 
85 


2411 

2572 
2729 


85 

85 
85 


2427 
2588 
2745 


85 
85 
86 


2443 
2604 
2760 


86 
85 
85 


2459 

2620 
2776 


85 

85 
85 


2476 
2635 
2791 


85 
85 
86 


2492 
2651 
2807 


85 2507 
85-2667 
85-2822 


85 

85 
86 


2524 
2682 
2838 


85-2540 
85-2698 
85-2863 


205 
206 
207 


85 
85 
85 


2868 
3020 
3170 


85 
86 
85 


2884 
3035 
3184 


86 
85 
85 


2899 
3061 
3199 


86 
85 
85 


2915 
3066 
3214 


85 
85 
85 


293C 
3081 
3229 


86 
85 


2945 
3095 
3244 


85 
85 
86 


2960 
3110 
3258 


85 2975 
85-3125 
85-3273 


85 

85 
85 


2990 
3140 

3287 


85-3005 
85 3165 
85-330a 


208 
209 
210 


85 
85 
85 


3316 
3460 
3601 


85 
85 
85 


3331 
3474 
3615 


85 
85 
85 


3345 
3488 
3629 


85 
85 
86 


3360 
3503 
3643 


85 
85 

85 


3373 
3517 
3657 


85 
85 
85 


3388 
3531 
3671 


86 
85 

85 


3403 
3546 
3685 


86 3417 
85-3559 
85-3698 


85 
85 
85 


3431 
3573 
3712 


85-3446 
85-3581 
85 3726 


211 
212 
213 


85 
85 
85 


3740 
3876 
4010 


85 

85 
88 


3754 
3890 
4023 


85 
85 
85 


3767 
3903 
4036 


85 
85 
85 


3781 
3917 
•4049 


85 

85 
85 


3795 
3930 
4063 


85 

85 
85 


3808 
3943 
4076 


85 
85 
85 


3822 
3957 
4089 


85 3836 
85 3970 
85-4102 


85 

85 
86 


3849 
3983 
4115 


85-3863 
85-3996 
85 4128 


21^ 
215 
216 


85 
85 
85 


4141 

4271 
4398 


85 
85 
85 


4154 
4284 
4411 


85 
86 
85 


4167 
4297 
4423 


85 
86 
85 


4180 
4309 
4436 


85 
85 
85 


4193 
4322 
4448 


85 
85 
85 


4206 
4335 
4461 


85 
85 
86 


4219 
4348 
4473 


85-4232 
85-4360 
85-4485 


86 
85 
85 


4245 
4373 

4498 


85-4258 
85-4385 
86-4510 


217 
218 
219 


85 
85 
85 


4523 
4645 
4766 


85 
85 

85 


4535 

4658 
4778 


85 
85 
85 


4547 
4670 
4790 


85 
85 
85 


4560 
4682 
4802 


85 
85 
86 


4572 
4694 
4814 


85 
85 
85 


4584 
4706 
4825 


85 
85 
85 


4597 
4718 
4837 


85-4609 
85-4730 
85-4849 


85 
85 
86 


4621 
4742 
4861 


86-4633 
86-4754 
86-4873 


220 
221 
222 


85 
85 
85 


4885 
5001 
5116 


85 
85 
85 


4896 
5013 
5128 


86 
85 
85 


4908 
5024 
5139 


85 
86 
86 


4920 
6036 
6150 


85 
85 
85 


4932 
5047 
5162 


86 
85 
85 


4943 
5059 
5173 


85 
85 
85 


4965 
6070 
6184 


85-4967 
85-5082 
85 5195 


86 
85 
86 


4978 
5093 
5207 


85-4990 
85-6105 
85-5218 


223 
224 
225 


85 
85 
85 


5229 
5340 
5449 


85 
85 
85 


5240 
5351 
5460 


85 
85 
85 


5251 
5362 
5470 


85 
85 
85 


5262 
5373 
6481 


85 
85 
85 


5273 
5384 
5492 


85 
85 
86 


5285 
5394 
5502 


85 
85 
85 


5296 
5405 
5513 


85-5307 
85-5416 
86-5624 


86 
85 
85 


5318 
5427 
5534 


85-5329 
86-5438 
86-6545 


226 
227 
228 


85 
85 
85 


5556 
5661 
5765 


85 
85 
85 


5566 
5672 
6775 


85 
85 
85 


5577 
5682 
5785 


85 
85 
85 


5688 
6693 
5796 


86 
85 
85 


6598 
5703 
5806 


86 
85 
85 


5609 
5713 
5816 


85 
86 
86 


5619 
5724 
5826 


85-5630 
85-5734 
85-5836 


85 
85 
85 


5640 

5744 
5846 


85-5651 
85-5755 
85-5856 


229 
230 


85 
85 


5866 
5966 


85 
85 


5876 
5976 


85 
85 


5886 
5986 


85 
85 


5896 
5996 


85 
85 


5906 
6006 


85 
85 


5916 
6015 


85 
85 


6926 
6025 


85 5936 
85-6035 


85 
85- 


5946 
6045 


85-5956 
85-6055 



XXI. — VARIETIES OF CANNON. 



CHAPTER XXI. 

VARIETIES OF CANNON. 

CLASSIFICATION. 

The numerous ways in which cannon may be classified 
have been simpHfied by the almost universal adoption of 
those which are breech-loading rifies^ built up of steel. 

For convenience of treatment we may consider them ac- 
cording to t\\Q\v proportions, construction and service, 

1. Proportions. 

The facility with which breech-loading cannon of all 
lengths may be loaded has practically abolished the distinc- 
tion between mortars and howitzers, although both terms are 
still used for pieces which do not differ materially in their 
proportions. 

It has become customary to distinguish guns (Chapter I) 
from howitzers by calling the first named rifles, although all 
new howitzers are also rifled. 

2. Construction. 

As to construction, cannon are divided into muzzle-loaders 
and breech-loaders; some of the former class being still re- 
tained in service pending the preparation of those of the better 
type and also for subordinate purposes. 

Breech-loaders may be divided into those having but one 
barrel, or single fire pieces, which are loaded by hand, and 
into machine guns, in which the loading is automatically per- 
formed by machinery. The former may be either the com- 
paratively slow fire cannon, in which the cartridge and 
projectile are loaded separately, or the rapid fire in which 



XXI. VARIETIES OF CANNON. 



the ammunition makes but one package, as in small arms, 
and the recoil of which does not derange the aim. 

Machine guns generally consist of a number of barrels so 
disposed, that while one is firing, the remainder may be 
loaded and prepared for loading. Like the rapid fire cannon 
these require metallic ammunition, and unlike them their size 
is imited by the weight of the required number of cartridges 
which can be conveniently kept in motion by the machinery ; 
the latter is generally operated by hand. 

3. Service. 

According to their employment, cannon are divided into 
those for the mountain, field, siege and sea coast services. 

The principal distinction here refers to the difficulties of 
transportation, for the rule is general that the most power- 
ful cannon that can be efficiently transported should always 
be employed. 

For field artillery especially, the principle of independence 
of function requires a very exact adaptation of the weight of 
the arm to the service required of it. Thus, we have, 1st, 
Horse Artillery, which, the cannoneers being mounted on 
horses, may accompany the Cavalry ; 2nd, Light Field Ar- 
tillery, which manoeuvres with Infantry ; and 3rd, Heaiy Field 
Artillery, which forms batteries of position at important tacti- 
cal points, and is intended to engage at long ranges. 

This affords the following table : 

CLASSIFICATION OF ARTILLERY ACCORDING TO 

1 P.-r,^^rt;r.nc S Guiis, for direct fire. 

1. rioporuons ^ Howitzers, or Mortars for curved fire. 

r Muz de loading ^Smoothbore. 

I (obselete, retained) \ Rifled. 

2. Construction \ ' i c- „, <-_ ( slow. 



' * ( ■ ( slow, 

j Breech loading rifles ) ^'"^le fire | ^.^p- j^ 
( Machine guns, 



XXI. — VARIETIES OF CANNON. 



3. Service. 



Mountain. 

i Horse Artillery, very light. 
Field < Light Field Artillery, medium. 

f Heavy Field Artillery. 
Siege. 
Sea Coast. 



SYSTEM OF ARTILLERY. 



This term refers to the character and arrangement of the 
materiel* as adopted by a nation at any particular epoch. 

The principal requisites of a system of artillery are sim- 
plicity^ mobility and power. To these the enormous arma- 
ments of the present day may add economy. 

The improvements of the last four hundred years have had 
these qualities in view, the compromises between simplicity 
and mechanical efficiency, noted Chapter XVI, causing 
sometimes one, and sometimes another of these qualities to 
pieponderate. 

As in other nations the system of artillery in the United 
States service is still in an experimental state. 

For lack of funds, withheld largely because of uncertainty 
regarding the direction of improvement, many obsolete 
weapons have been retained by us either unchanged, or 
converted so as to increase their power at a moderate expense. 

The following description is therefore partly historical, and 
contains incidental reference to methods adopted in other 
countries whose political situation has made their immediate 
armament urgent. It is confined to slow fire guns, since 
other types of breech-loaders depend for their efficiency 
almost wholly upon the control of their recoil and upon the 
use of metaUic ammunition; subjects not yet discussed. See 
Chapter XXIX. 

* See Webster, 



XXr. — VARIETIES OF CANNON. 



CONSTRUCTION. 

I. MUZZLE LOADING CANNON. 

United States. 

The field guns used during the Civil War were of two 
kinds. 

1. The 3 ijich wrought iron (10 pdr^ rifle. 

This was made by wrapping boiler plate around a wrought 
iron bar to form a rough cyUnder, which was welded 
together under the rolls and finished in the usual manner. 

It made a very strong, light gun well adapted to the 
Horse Artillery. 

2. The 12 pdr. Napoleon Gun^ S7nooth bore. 

This was of bronze, cast solid. Its value depended upon 
the topography of the seat of war. 

The broken surface of the Appalachian system and the 
heavy woods with which much of the country was covered 
restricted the fighting to ranges which, compared to those 
obtainable on the broad plains of Europe, are very moderate. 
For such ranges its heavy shell and well filled shrapnel were 
more efiective than those of the rifle, and the initial velocity 
was so great that for ranges of about 1000 yards the trajectory 
of the smooth bore was flatter than that of the rifle. 

The siege gims, in which mobility was less important, were 
of cast iron. Owing to the length of the bore and its rela- 
tively small diameter these guns were cast solid. The pro- 
jectile weighed about 30 pounds. 

One of these pieces, the Parrott, was strengthened by a 
wrought iron cylinder shrunk over the breech and reinforce. 

In order to prepare so massive a forging a hot iron bar was 
coiled helically around a mandrel, brought to a welding heat 
and forged by axial blows of the hammer. To prevent 



XXr. — VARIETIES OF CANNON. 



distortion during welding, the coil was held in a hollow cyl- 
inder. Several coils would be similarly welded end to end. 
The direction of the fibers gave great tangential tenacity, but 
for reasons given in Chapters XV, page 60, and XIX, page 
12, the construction was faulty. 

Sea coast guns were generally of cast iron, cast hollow on 
the Rodman principle. To some the Parrott construction 
was applied. 

Since 1875 many Rodman guns have been converted on 
the Palliser (English) plan by reaming out the bores to receive 
a thick, wrought-iron tube, which was then rifled. Chapter 
XIX. 

These tubes, first made by coiling as above described, were 
ultimately replaced by those of solid steel, the intrinsic 
strength of which was almost sufficient. 

The wrought-iron tube was at fiist inserted from the muzzle ; 
but, as it was liable to be carried out with the projectile, a 
stronger but much more costly breech insertion was employed. 

With steel, which presented no false welds for the action 
of the powder gases, the muzzle insertion was resumed. 

In this way many 10 inch smooth-bore Rodman guns were 
altered to 8 inch rifles. The 15 inch Rodman guns are re- 
tained unchanged for subordinate purposes. 

Foreign Services. 

Abroad a similar course was followed. In France^ the old 
cast-iron guns were hooped with puddled steel, originally to 
retain the fragments on explosion. The bores were lined 
with a short steel tube. This method is now followed for 
subordinate pieces of large caliber. 

Engla7id tried the Palliser plan of conversion for her old 
guns. For new guns wrought iron was at first exclusively 
employed ; then wrought iron coils on a steel tube were used, 



XXI. — VARIETIES OF CANNON. 



and finally with breech loaders steel throughout. The fear 
of the brittleness of steel, the consequent preference for the 
weaker though more ductile wrought iron, and the indiffer- 
ence to the molecular treatment of steel as practiced by their 
more exact neighbors, the French, have cost the English 
Government much loss in time and money. 

To Krupp, in Germany, belongs the credit of first using 
steel in large masses. The weight of his ingots has increased 
since 1851 from two tons to seventy. 

The construction of his cannon now requires relatively 
large units of construction. The tendency elsewhere is to 
reduce the weight of the maximum unit so as to avoid the 
large outlay for plant required only for its manufacture and 
handling. For it must be remembered that although cannon 
comprise the heaviest masses now made, yet their commercial 
importance is relatively small. Chapter XIV, page 2. 

II. BREECH LOADING CANNON. 

These may be classified according to the means by which 
the breech is closed ; but, as this depends largely upon the 
form of gas check employed, this will be first discussed. 

1. Gas Checks. 

Many early efforts were made to prevent the escape of gas 
by some rigid fastening after the manner of a plug ; but, owing 
to the erosion through the slightest crevice caused by dust, 
rust or fouling, the efficiency of these devices was short-lived. 

The self-sealing gas check alone made breech loading prac- 
ticable. Gas checks may be classified according as they are 
attached to or detached from the breech block. 

Detached Gas Checks. 
The ordinary metallic cartridge case is the best example of 
this class. The flexibility of its walls and its renewal at every 
fire peculiarly adapt it for this purpose. 



XXI, — VARIETIES OF CANNON^ 



But, since it would be impracticable to use cartridges of 
the size required for heavy cannon, the cartridge case may be 
replaced by a short permanent ring as shown in figure 1. 

This represents one form of an American invention, the 
Broadwell ring, r, with its obturator plate, /. 

The gaseous pressure expands the thin edge laterally 
against the seat in the tube and also presses the ring bodily 
backward against the plate. The annular grooves, g, in the 
base of the ring serve as air packing ; they also increase the 
intensity of the pressure on a vital surface, and, with the hol- 
low, h, collect any fouUng, which might otherwise occur on 
this surface. 

The surface^ s, is spherical so as to adjust itself easily to he 
spherical seat of the ring around the mouth of the chamber, 
past which the obturator plate is caused to slide by the motion 
of the breech block to which it is attached. 

This form of gas check is difficult to maintain, as it is diffi- 
cult to prevent entirely the escape of gas between the ring 
and the plate. 

Attached Gas Checks, 

These necessarily require some motion of the block in the 
direction of the axis of the piece and across the joint to be 
sealed. 

Figure 2 represents the Freyre gas check of Spanish origin. 
It consists of a steel ring, r, of triangular cross-section sur- 
rounding a conical wedge, w. This last is formed with a 
spindle, 5, passing axially through the breech block, B, The 
stem is surrounded by a spiral spring against which it acts by 
a shoulder. The thickness of the wedge is slightly less than 
that of the ring. 

The gases press the wedge backward and thus expand the 
ring ; when they cease to act the spring moves the wedge 
forward and thus prevents the ring from sticking in its seat. 

Figure 3 represents the De Bange (French) gas check, de- 



XXI. — VARIETIES OF CANNON 



rived from that used in the Chassepot b 1, rifle, a small arm 
firing a non-metallic cartridge The steel ring of figure 2 is 
replaced by a plastic ring, r, composed of a mixture of asbes- 
tos and tallow enclosed in canvass and having the joints 
through which the composition might extrude protected by- 
metallic rings. When the mushroom head, h, is compressed 
axially the ring, r, expands laterally, giving a pressure per 

unit of area against the surface of its seat nearly equal to ^^-i- ; 

in which R is the common external radius of the head and 
ring, and / is the length of its bearing. 

A nut on the rear end of the spindle regulates the initial 
compression required for efficiency. A spring beneath the 
nut relieves it from shock as the head is thrown forward after 
firing by the elasticity of the tallow. 

^ Comparison. 

The Broadwell ring has to seal four surfaces not protected 
from dirt instead of but two, and the joint, most difficult to 
seal, is that which is most exposed to dirt. 

Of the attached gas checks, the Freyre, being inorganic, is 
less subject to extreme variations of temperature ; it also takes 
up less room in the thickest part of the gun. It is open to 
objection that a sHght nick on the edge of the ring might 
render the entire apparatus worthless. 

To the last consideration is due the almost universal 
employment of the De Bange gas check, since this has been 
found almost indestructible by the accidents of service and to 
resume its shape when deformed in firing. 

2. Fermeture. 

The fermeture (French, fermer to close) is the device by 
which the breech is opened and closed. Its principal requi- 
sites are safety and convenience. The form of fermeture 
depends largely upon the kind of gas check employed. 



XXI. — VARIETIES OF CANNON. 



Two principal varieties exist, the Krupp and the French 
systems. 

1. The Krupp or wedge system, figure 4. 

Description. 

The breech block, B^ moves transversely through a hori- 
zontal slot in rear of the chamber. The front face of the 
block is flat, and the rear surface a convex semi-cylinder whose 
axis is slightly inclined to the plane of the face. This avoids 
the sharp reentrant angles noted. Chapter XV, page 21. It 
has been found expedient also to round the angles in front 
of the slot. 

The upper and lower surfaces of the slot contain guides, ^, 
which are parallel to the elements of the cylindrical surface 
and enter corresponding grooves in the block. The block 
thus receives a component longitudinal motion in the direc- 
tion of the axis of the bore which prevents friction between 
the ring and the obturator plate, and also assists somewhat in 
pressing the cartridge home. 

A hole, h, through the block permits the gun to be loaded 
when the block is withdrawn to the proper position. It is 
prevented from passing this point by a stop bolt, screwed 
through the body of the gun and having a blank end pro- 
jecting into a groove on the upper surface of the block. 

Locking. 

To secure the fermeture a revolving latch^ /, is employed. 
For small cannon using metallic ammunition this may be a 
simple turn-button operated by an exterior handle, (9, and 
entering a recess in one of the faces of the slot. 

With a less perfect gas check, means must be provided for 
pressing the obturator plate, /, against the ring, r, so that 
for larger guns the latch consists of a screw. In order to 
faciUtate the operation of the fermeture, the fillets on one 



10 XXI. — VARIETIES OF CANNON. 

side of the newel of the screw are removed so that a half- 
turn of the screw may engage or disengage the remaining 
fillets. 

Translation. 

For field pieces the block is withdrawn directly by hand, 
but heavy pieces are provided with a long screw, S^ con- 
tained in a groove in the upper part of the block, and turn- 
ing in two cylindrical collars, one at each end. The rotation 
of this screw in a half nut which is attached to the gun, 
causes relative motion to occur between the block and the 
gun. 

Since for this motion speed is required, the screw is cut 
with a considerable pitch. As this causes a loss of the power 
required to start the block from its seat and to close it firmly, 
there is supplied an auxiliary locking screw, d^ which passes 
through the latch, /. By a peculiar arrangement illustrated 
in a model in the Ordnance Museum, in closing the breech 
this screw first turns the latch and then by its slow pitch 
supplies the power required, and conversely in opening. 

Both screws are operated by a T wrench, G, which is 
detached. 

2. The interrupted screw fermeture is commonly 
known as the French system, although its origin is probably 
American. 

Description. 

A cylindrical block fills the breech in the prolongation of 
the bore and in rear of the tube. 

The block is held by a screw thread which engages with 
the base ring ; this in turn is screwed to the jacket by a 
ratchet screw thread, Chapter XV, figure 47, and figures 2, 3 
and 10, Chapter XXI. 

To facilitate its operation, alternate sections, ordinarily of 



XXI. — VARIETIES OF CANNON. 11 

60", are removed from the adjacent surfaces of the block and 
base ring, so that after sUding the block nearly into place it 
may be easily locked. 

Some device is required to support the block when with- 
drawn. For small pieces this is supplied by the carrier ring. 

This ring is provided with two lugs forming, with corre- 
sponding cavities in the jacket and a vertical pin, a hinge on 
which it swings to the left and rear in opening. 

A stop^ a b^ Chapter XV, figure 47, screwed to the carrier 
ring, enters a groove formed in one of the smooth sectors of 
the block. This groove terminates in front at a short dis- 
tance from the face of the block, and in rear makes a return 
of 60° parallel to the screw thread. 

The carrier ring also contains a shallow groove, c d, for 
the head of the lever, and the latch, /, the action of which is 
important. See figure 10. 

The latch is pressed by a spiral spring radially inward 
against the block, so that its inner extremity describes on the 
smooth sector on which it rests a path parallel to the groove 
in which travels the stop. We will designate the rearmost 
end of this path by r, and the front end by /. At r and / 
are formed cavities into which the inner end of the latch may 
enter sufficiently to sink its outer end to the level of the outer 
edge of the carrier ring. Each cavity is connected with the 
intervening path by an inclined plane ; the cavity at / is prac- 
tically a cylinder. 

On the rear face of the base ring is a conical dowel, the 
point of which, when the carrier ring is closed, enters a corre- 
sponding cavity in the adjacent face of the carrier ring. 
After passing this cavity, the point of the dowel enters a 
conical hole in the front surface of the latch, and thus serves 
to press it radially outward, so that when the carrier ring has 
been completely closed, the inner end of the latch will have 
been raised so far out of the cavity / that the block may slide 



12 XXI. VARIETIES OF CANNON. 

freely through the carrier ring. As it slides it forces the 
outer end of the latch into its seat in the jacket. 

There are three concentric pieces, the block, the carrier 
ring and the jacket. The latch unites these alternately in 
pairs. 

Operation. 

Suppose the block to be closed and locked. Raise the 
lever and turn the block to the left until the stop prevents 
further rotation. 

In so doing, the inner end of the latch rides up the inclined 
plane leading from r, and the outer end enters the jacket as 
shown in the end view of figure 47, Chapter XV. This pre- 
vents the obstruction to the withdrawal of the block caused 
by the simultaneous swinging of the ring which would other- 
wise occur. 

The block can now ordinarily be freely withdrawn ; but if, 
from the expansion of the gas check, it should not move 
freely, an eccentric projection on the head of the lever acts 
as a cam''^ and starts the block from its seat. 

It is well to observe that the rotation of the block being 
independent of that of the gas check, the binding of the 
latter does not 'resist the initial rotation above described. 

On withdrawing the block to the extent allowed by the 
stop grove, the inner end of the latch drops into the cavity 
f ; the carrier ring is then free to swing in continuation of 
the motion of withdrawal. 

After loading, these motions are reversed. In closing the 
breech the latch locks the block and carrier ring together, 
since any slippipg of the block through the ring would cause 
the edge of the gas check to strike against the base ring. 
This would be particulariy objectionable in the Freyre check. 

When the carrier ring comes against the rear face of the 



* See Webster. 



XXI. — VARIETIES OF CANNON. IB 

base ring the conical pin described lifts the pin from the hole, 
/, and permits the block to slide forward until ready to en- 
gage with the threads in the base ring. 

After closing the breech the eccentric head of the lever 
enters the groove, c d ; this prevents the unscrewing of the 
block by the tangential component of the pressure on the 
screw threads. This pressure is so great that it has been 
found necessary to protect the bearing surface of the groove, 
^^, by a plate of hardened steel.* 

Variations, 

For large pieces a more stable support than that offered by 
the thin carrier ring is required during the withdrawal of the 
block. 

This is furnished by a tray which supports it for its whole 
length. 

This tray is supported by a hinge bracket, called the coit- 
sole, which, being fastened to the face of the breech, allows 
the block and tray to be swung aside. 

For such pieces the simple lever used in the field piece 
affords insufficient power. 

It is accordingly replaced by more or less complicated 
machinery which, for the largest calibers, may be operated by 
steam, hydraulic or electrical power. 

One of the most ingenious devices is that of the French 
engineer, Canet, who has an apparatus in which the contin- 
uous rotation of a crank performs all the varied operations 
of unlocking, withdrawing and swinging the block. 

Vent. 
The system adapts itself to the use of an axial vent which 
facilitates ignition. To permit renewal, the vent piece is 

* The latest model (1890) exhibits slight changes in the details of the 
construction shown in figure 47, Chapter XV. 



14 XXI. — VARIETIES OF CANNON. 



made removable ; and to avoid erosion, its front portion is 
of copper. 

To avoid the danger of a premature discharge, the vent is 
preferably protected by a sliding shutter, a projection from 
which travels in a concentric groove in the rear face of the 
piece which is so formed that the primer cannot be inserted 
until the block is securely locked in place. 

The complication attending the operation of an axial vent, 
the likelihood of accident to the gunners from the projection 
of the fragments of the ordinary primer and the necessary 
delicacy of the safety shutter when made on the small scale 
required for the field gun have so far caused these guns to be 
provided with a radial vent piece of copper leading to the top 
of the charge at about half its length. 

Base Ring. 

The seat of the block is of somewhat greater diameter than 
that required for loading in order to give a large bearing sur- 
face to the threads of the screw. 

Under Barlow's law, this surface is less dilated by the gas 
pressure than one nearer to the axis ; and, since from a simi- 
lar reason the greatest stress is borne by the foremost fillets, 
these do not approach as closely to the end of the tube as 
the construction might otherwise permit. 

All exposed screw threads have their angles rounded, to 
avoid fracture and to resist deformation by the projectile in 
loading. For heavy pieces a loading tray is slipped into the 
opening so as to cover the thread in the base screw while the 
projectile is being pressed home. 

The operation of the gun is very much facilitated by de- 
vices which avoid the translation of the breech block. One 
of these consists in giving the breech block a general conical 
shape so that it will swing directly into the position for 
locking. 



XXI. — VARIETIES OF CANNON. 16 

The same end is accomplished in the Gerdon fermeture, 
figure 13, now on trial in the United States. After revolving 
the block through 90° so as to clear the two threaded sectors, 
it is swung to one side through a slot cut in the jacket. A 
radial slide on the rear face of the block acts both as a latch 
and as a shutter to the axial vent. 

The parts are remarkably few and simple. 

Comparison of the Two Systems. 

1. Except where metallic ammunition is employed the 
French system permits the use of the best gas check. 

2. It diminishes the weight of the gun for a given value 
of u and d. Chapter XII. 

3. It serves to press the cartridge into place instead of 
guillotining it as in the Krupp. 

4. The fermeture, when open, is less exposed to injury 
from a front fire. 

5. It may be worked by power. 

The Krupp system in its conception is of almost rustic 
simplicity. 

This advantage is counterbalanced by the inferior gas 
check which is required when non-metallic ammunition is 
employed ; also by the thickness and mass of the forging 
containing the slot, the presence of which must cause inju- 
rious internal strain in oil hardening. 

The jar in opening it suddenly may deform and even bend 
the stop bolt. The parts are less securely protected in travell- 
ing. It has also the comparative disadvantages named in the 
discussion of the French system. The danger of premature 
discharge, though not so great as in the French system, is still 
said to exist. 



16 XXI. — VARIETIES OF CANNON. 



U. S. SYSTEM OF ARTILLERY. 

MOUNTAIN SERVICE. 

The Hotchkiss 1.65-inch Rifle. 

This gun weight but a Httle over 100 pounds and its car- 
riage about twice as much, so that either makes but a fair load 
for a mule. Metallic ammunition is employed > The gun is 
a single piece of steel provided with the simplest form of 
Krupp fermeture as shown in figure 5 The operation of the 
fermeture can be readily seen from the figure and from pre- 
vious discussions. 

Its special feature is the extractor, x. This is a prismatic 
bolt, a hook on the front end of which engages with the 
flange of the cartridge (Chapter XVI, figures 8 and 9) as this 
is loaded 

The extractor slides in a longitudinal groove, g, on the 
upper surface of the slot On its lower face is a tenon which 
enters a transverse groove, g' , in the upper face of the block. 

The groove, g' ^ near the handle is straight and slightly 
inclined to the rear face, so as to give power in wedging the 
cartridge case from its seat. The screw thread on the latch 
also assists. At the other end it is so curved that when, in 
opening the breech, the loading hole comes opposite to the 
chamber the extractor will be suddenly drawn backwards, 
throwing the free cartridge case clear of the gun. The first 
of these operations is called the extraction, and the second 
the ejection 

For simplicity this piece is fired with the ordinary friction 
primer. The blast from this raises the central portion of a 
thin, cup-shaped gas check within the cartridge, and the 
flame passes through the three holes shown in figure 8, Chap- 
ter XVI. As soon as the charge is ignited the back pres- 
sure of the gases closes the vent by reversing the action of 
the gas check, 



XXI. — VARIETIES OF CANNON. 17 



Hotchkiss 3-Inch Mountain Rifle. 

In order to permit the use of shrapnel a heavier mountain 
gun of 3-inch caUber has been recently produced. Figure 11. 

Foreign Variations, 
In order to increase both the power and portability of 
mountain cannon they are frequently made abroad in sections 
which are screwed together before firing. " Screw-guns " of 
8-inch caliber have been successfully fired . 

FIELD SERVICE. 

The 3.2 B. L. Rifle shown in Chapter XV, figure 47, is 
the only new field piece now issued. (1891.) It is eventu- 
ally intended for use as a Horse Artillery gun, and to be 
replaced for Field Service proper by a similar gun of 3.6 
in caliber, firing a 20-pound shell. A 3.6 B. L. Mortar, 
figure 12, firing the same projectile, is also contemplated for 
delivering vertical fire against troops sheltered by temporary 
defences. It has a range of nearly two miles. 

Foreign Variations. 
It is proposed in France to have but one caliber, about 
3 in. for all mountain and field service, viz., short, light, 
long and heavy pieces. 

SIEGE SERVICE. 

Siege cannon are intended for attacking and defending 
inland fortifications and the land fronts of sea- coast fortifi- 
cations. 

The term is usually applied to pieces which, although too 
heavy for field operations, are yet light enough to be trans- 
ported over common roads upon the carriages from which 
they are fired. 

This limits the weight of the gun and carriage together to 
that which may safely be transported across a pontoon bridge. 



18 XXI. VARIETIES OF CANNON. 

Siege Gun. 

The 5-inch siege rifle, figure 6, resembles in its construction 
the field gun described. 

Siege Howitzer. 

Principles of Design, 

Defences of masonry have been largely replaced by those 
which are armored, or, particularly for the besieging party, 
of earth. 

While armor requires for its penetration the concentration 
of kinetic energy found in a projectile of relatively small 
diameter fired from a gun, the demolition of earth works 
demands rather the transfer of energy in the potential form. 
Such defences should therefore be attacked by cannon of 
the largest caliber consistent with portability. 

If the maximum weight of the piece is fixed by the con- 
siderations previously named, then by the definition of 
Chapter I, a howitzer results. 

The proportions of this piece are also demanded by the 
advantages pertaining to vertical fire againt the large and 
well defined area occupied by the besieged, against com- 
munications of the besieger which are screened from view, 
and against the roofs of turrets. The shorter the piece is 
in rear of the trunnions the more easily may high angles 
of fire from a given carriage provided with the ordinary 
elevating screw be attained.* The avoidance of preponder- 
ance and the requisite strength of the chase demand that 
the length in front of the trunnions be also reduced. 

Such considerations have fixed the value of u at about 
12 times the caliber, which is 7 inches. 

It is intended to throw a projectile weighing about 100 
pounds to a distance of about 3 miles. 

*A new German howitzer has the trunnions placed ahuost at the breech. 
In this carriage the elevating screw is under the chase, as the arrange- 
ment adopted gives a considerable muzzle preponderance. See also Car- 
riage for 7-inch Howitzer, Chapter XXIII, figure 6. 



XXK — VARIETIES OF CANNON. 19 



Owing to the strength of the construction a larger cahber 
might have been employed for the given weight, but in such 
a case the energy. of recoil, (Equation 7, Chapter XIX,) 
would have been excessive. 

Since with the value of /„ usual in built up steel guns, the 
short length of bore reduces the value of e^ it is proposed to 
utilize the value of E permitted by the strength of the car- 
riage by increasing the value of ;//. 

This will permit the use of very long torpedo shells 
(Chapter XVI, page 20). The limit of E for the wheeled 
carriage having thus been reached, for high angles of fire 
which increase the stress upon the axle, E may be further 
increased by dismounting the wheels and laying the stock of 
the carriage on a platform It is now (1891) proposed to use 
in the field service a 6 inch B. L mortar throwing a 70 
pound shell, to be mounted as above described 

It is probable that in the future the obstruction to effi- 
ciency which is due to the requirement that the piece be 
transported on the carriage from which it is to be fired, will 
disappear before the adoption of special carriages designed 
with the view of efficiently satisfying their independent 
requirements. 

Charges. 

In order to vary the angle of fall* to suit the range and 
the kind of fire employed, the howitzer is fired with varying 
charges of powder as well as with varying angles of fire. In 
this it differs from the gun in which the charge is usually a 
constant and a maximum. See Chapter XXX, page 9. 

7-Iiich B. L Howitzer 

The construction, figure 8, resembles that of the field piece, 
the principal difference being in the construction of the key 
ring. This consists of two semi-circular segments of rect- 

*The angle with the horizontal made by the tangent to the trajectory 
on impact. 



20 XXI. — VARIETIES OF CANNON. 

angular cross-section which are laid in a shallow groove in 
the tube so as to project above its exterior and to bear 
against the front face of the trunnion hoop. They are kept 
in place by the lap of the sleeve. 

The friction developed by shrinkage between the jacket 
and the tube throws part of the longitudinal stress upon the 
tube from which the key ring transfers this stress to the 
trunnions. 

A shoulder formed on the tube in rear prevents the for- 
ward motion of the tube from the friction between it and the 
projectile. See page 5. This feature is general, 

The cavities in the ends of the trunnions are for the points 
of the bailm which the piece is slung in mounting. 

SEA COAST CANNON. 

These comprise rifles of and above 8-inch caliber, and 
12-inch rifled mortars, 
Eifles. 

Figure 7 shows the 8-inch b 1. steel gun with which most 
of the recent experiments have been made. 

The construction resembles that heretofore discussed, 
except that the jacket is strengthened by two rows of hoops, 
which since the original design, have been extended to the 
muzzle. (Chapter XI, page 18, paragraph 4.) 

Other S. C, Rifles. 

The guns so far designed are of 8, 10, 12 and 16-inch 
caliber. Being intended for use with the largest charges of 
slow burning powder, they are made very long, the values of 
u ranging from about 24 to 27 calibers. 

For the largest calibers it is proposed to dispense with 
trunnions which are to be replaced by several rows of cir- 
cumferential ribs, by which, as in cannon of the very earliest 
iimeSy the pieces are to be secured to their support. The 
necessary alterations in elevation will be given by varying the 



XXI. — VARIETIES OF CANNON. 21 

inclination of the chassis, to which by this arrangement the 
recoil is always parallel. 

Mortars. 

The importance of nearly vertical impact against the 
decks of vessels at short ranges requires the mortars to fire 
with angles of elevation as great as 75°. 

It is proposed to group them in sunken batteries of 12 or 
16 mortars, united under the control of one officer. He will 
occupy a detached position free from smoke, and will be pro- 
vided with an accurate range finder, and with means of com- 
municating to the chiefs of pieces the direction and elevation 
required. A simultaneous volley from the battery will prob- 
ably drive from its anchorage any vessel within range. This 
will be an important aid to the defense, since, as the bom- 
bardment of Alexandria in 1882 clearly showed, the accuracy 
of fire from a vessel is much diminished when the vessel is 
under way. 

V2,-inch B. L. Mortar. {Figure 9.) 

The immediate supply of these cannon demanded by our 
present necessities (1891) and the relatively low energies 
required to penetrate armored decks by vertical fire have so 
far permitted the body of these pieces to be made of iron 
cast on the Rodman principle and strengthened by two rows 
of steel hoops as shown in figure 9. 

The recent failure at a pressure of less than 20,000 pounds 
of an unhooped 12-inch cast iron mortar would indicate the 
future use of steel throughout the piece as soon as the steel 
works and the gun factory shall have become able to supply 
a sufficient numl)er of heavy steel guns. 

The growing importance of vertical fire has caused the 
employment of mortars, even upon ship board, to be seriously 
considered. 

The value of u in this piece is about 6 calibers. 



22 



XXI. — VARIETIES OF CANNON. 



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XXII. — ARTILLERY CARRIAGES. 



CHAPTER XXII. 

ARTILLERY CARRIAGES. 

PRINCIPLES OF CONSTRUCTION. 

Classification. 

Artillery carriages may be classified according as they are 
intended to support the piece when fired, to transport it, and 
to supply it with ammunition and accessories. These func- 
tions are sometimes combined. 

They may also be classified according to the service in 
which they are employed. 
Requisites. 

1. Strength to resist permanent deformation from the shock 
of recoil. 

2. Stability in firing and on the march. 

3. Mobility as regards the ease of service in battery, and 
of transportation when required. 

4. Only a moderate recoil in firing, so as to facilitate the 
service of the piece and to avoid the exposure of the gunners 
when sheltered by defences. A compromise between these 
properties is often necessary. 

I. CARRIAGES WHICH SUPPORT THE PIECE. 

GENERAL DESCRIPTION. 

These are called gun carriages. They may be either sta- 
tionary or wheeled. 

Stationary Carriages. 

The simplest form exists in the iron mortar bed used for the 
old S. B. Mortars. 



X3tll. — ARTILLERY CARRIAGES. 



This consists of trapezoidal plates forming the cheeks^ which 
support the trunnions of the piece at such a height as to per- 
mit it to receive the elevation required. The cheeks are con- 
nected by transverse diaphragms called transoms and bolts in 
order to form a strong frame. For heavy pieces each cheek 
may consist of two plates united to a T shaped bar as shown 
in figure 1. The cheeks may be stiffened in the direction of 
compressive stresses by bars included between the plates. 

The bearings of the trunnions may be widened by trunnion 
bed plates^ so as to diminish the pressure per unit of area 
which they are called upon to support. The mortar bed is 
made low for ease of loading and for stability. The prin- 
ciples of construction above noted are of general application. 

Sea coast gun carriages are intended to be used in firing 
over a parapet or through an embrasure. In the first case 
they are called barbette carriages, and in the second, casemate 
carriages. Owing to the height of the piece above the 
ground and the low angles of fire employed, the stability of 
the system generally requires the support of the piece to be 
divided into the gun carriage proper, constructed like the 
mortar bed, and tlie chassis, which is a moveable railway 
capable of directing the piece in its recoil and of being trav- 
ersed in azimuth. 

Non-recoil carriages are separately treated hereafter. 

Wheeled Carriages. 

In the mountain, field and siege services, the gun carriage 
must also be adapted to transportation. This involves the 
use of wheels, which complicate the problem of controlling 
the recoil. 

Parts. 

Their essential parts are : — 

1, The stock. This is a prolongation of the cheeks which, 
with the wheels, forms the three points necessary for stability. 



XXII. — ARTILLERY CARRIAGES, 



A greater number of supports might affect the stability on 
uneven ground. 

The stock serves also to point the piece, since it sustains 
the elevating screw, and with the aid of the handspike gives 
the necessary changes in azimuth 

It also connects the front and rear wheels in transporta- 
tion. 

For modern carriages the stock consists of two sheet 
steel flasks or brackets which rest at the head of the stock 
upon the axle, and are united at the further end by the trail 
plate or shoe, 

2. The wheels and the axle replace the continuous support 
afforded in stationary carriages by the cheeks. 

PERIODS OF THE RECOIL. 

The recoil may be separated into two periods : 

1, That during which the projectile is acquiring energy in 
the piece. 

2. That comprising the subsequent recoil. Since the 
carriage is found not to move materially until the projectile 
has reached the muzzle, and since the system is not rigid, 
the corresponding phenomena may be taken to be : 

1. A series of shocks between the trunnions and their 
beds transmitted through the axles to the wheels and through 
the stock to the trail. The system is finally set in motion by 
these shocks. 

2. The resulting motion of the system accelerated by the 
remaining gaseous pressure and retarded by friction and 
various artificial resistances. 

Energy of Recoil. 

The nature of the recoil is preferably studied by veloci- 
meters of Class III. But, as this is difficult and requires the 
previous construction of the carriage, it is customary for 
theoretical discussions of a general nature to ignore the first 



XXII — ARTILLERY CARRIAGES. 



period, and to assume that the system is rigid and that the 
acceleration to the system during the second period is com- 
pensated for by the acceleration of the projectile noted in 
Chapter XI, page 18.* 

We may therefore change Equation (7), Chapter XIX, 
to read 

in which the subscript s refers to the entire system recoiling. 
For greater accuracy, when the mass of the powder, or 
m'^ bears a considerable ratio to that of the projectile, we 
may use the following formula in which v' represents the 
mean velocity of the products of combustion, found by 
experiment to be about 3,000 /. s. 

_ m V + m' v' 

Distribution of "Work of Eecoil. 

Since this work is distributed between the two periods, 
and since it is necessary to restrict the exent of the recoil, it 
becomes necessary, as in Chapter V, to determine the 
maximum stress which the system can safely endure and to 
maintain this stress as nearly constant as possible over the 
path of the recoil. 

This principle, which underlies all recent improvements, in 
gun carriages, owes its importance to the recent increase of 
m and e and the decrease m M (Equation 7, Chapter XIX), 
due to the general use of built up rifled cannon firing large 
charges o^ progressive powder In fact, it may be said that 
the limit of the power of cannon, or h, page 21, Chapter XI, 
is fixed by the difficulty of controlling their recoil, 

If we assume that the mobility of the system fixes the sum 
of the masses, M and J/', composing the gun and carriage, 



This assumption will be corrected as occasion arises hereafter. 



XXII. ARTILLERY CARRIAGES. 



the following discussion explains the prevailing practice of 
making M' approximately equal to M. 

For, if we assume the carriage to be properly proportioned, 
general experience shows that its permanent deformation, Q, 
may be considered inversely proportional to its mass and 
directly proportional to the energy which it receives. So that 

liM-{- M' =z C, Q will be least when M — M'. 

The assumption on which this deduction is based, although 
confirmed by experience in the construction of carriages, an- 
vils and armor, is not conclusive ; since mechanical ingenuity 
may compensate for the loss of strength resulting irom a 
diminution of M' . 

REMARKS. 

It is found that with quick powders the velocity of recoil 
during the first period is greater than with slow powders, the 
maximum momentum of the projectile being the same. 

With slow powders the velocity during the second period 
is increased to such an extent by the high pressure as the 
projectile leaves the gun (Chapter XI, page 18), that special 
devices have become necessary to diminish the increased 
extent of the recoil. 

The problem is so complicated that computations, princi- 
pally by graphical methods, are mainly resorted to in order 
to determine the direction of the stresses, the corresponding 
dimensions being found empirically. It is highly probable 
that the gun carriages of the future, like many other construc- 
tions, will be the outgrowth of practical experience. 

FORCES ACTING ON A GUN CARRIAGE. 

Velocity of Translation. 

If the axis of the bore intersects the axis of the trunnions 
at the centre of gravity of the piece, the force producing re- 



XXII. ARTILLERY CARRIAGES. 



coil is communicated to the carriage at the trunnion beds. 
The carriage being constructed symmetrically with regard to 
the axis of the piece, we may suppose that the wheels, trun- 
nion beds and trail are all situated in the same plane and that 
the force producing recoil is applied at the point where the 
axis of the trunnions pierces this plane. 

The direction in which this force acts will be that given by 
the angle of fire or the inclination to the horizontal of the axis 
of the piece. 

Let V figure 2, be the position of the axis of the trunnions, 
and mv-=.I,^ represent the intensity and direction of the 
force, and Q the angle of fire. Let Z'be the point of contact 
of the trail and ground, / the distance of this point from the 
trunnions, and a the angle made by the line Tv, with the 
horizontal. Let W^ be the weight of the system acting 
through the center of gravity G at the horizontal distance b 
from the point T. Let/ be the coefficient of friction between 
the carriage and the horizontal platform on which it rests. 

The vertical component of /, , and W^ will cause friction 
between the carriage and the platform. The force of friction 
or/(^g 4" '^^ ^ s^'^ ^)' wil^ oppose motion. So that, repre- 
senting by Fthe horizontal velocity of recoil, we have 

y. m V cos 6 — / ( ^8 4~ ^^^ ^ sin B) 
m V (cos — / sin 0) 

in which g f may be neglected. 

The vertical component will be distributed along the sup- 
ports in a manner determined by the construction of the car- 
riage and the values of Q. For wheeled carriages /will have 
separate values for the wheels and the trail. 

If, in Equation 4, we neglect the weight of the system in 
comparison with the vertical component of 7, , (or g /), we 



XXII. — ARTILLERY CARRIAGES. 



find that V will reduce to 0, or that recoil will cease for a 
value of 0, such that, calling this angle 0, 

tan e, = y (5) 

This is called the angle of no recoil. 

Extent of Recoil. 

The extent of the recoil will be 






s=^-^.' (6) 



If, as is usual, the platform be inclined at an angle, /3, with 
the horizon so as to check the recoil, then for 6 in the above 
equations should be written 

d + (3; and for F, Tcos 3. 

In this case, since the energy of the recoil is absorbed not 
only by friction but by the work done in lifting JV^ through 
a height = s sin (3, we have 

Fcosfi' 



2 g (sin (3 + / cos (i) 



(J) 



These equations are said to give correct values for stationary 
carriages, but do not apply very exactly to those which are 
wheeled. 

Angpilar Velocity. 

The force, /, , also acts to rotate the carriage around 
the point T with a moment proportional to its lever arm, 
/ sin (a — 6), so that the moment of this force will be 
m V Isin (a — 6). 

This is opposed by the moment of the weight, or JV^ b. 
Then, since the angular velocity of the system is equal to 
the resultant moment of the impressed forces divided by the 
moment of inertia of the system, we have, representing the 



XXII. — ARTILLERY CARRIAGES. 



angular velocity, about T by o) and the corresponding radius 

of gyration by k. 

mvl sin (a — Q\ — W^ b 
--S '-j^J •- (8) 

With this relation we may discuss in an elementary manner 
the stability of the system. For example, in the old S. B. 
Mortars, since W^ is small, a is made less than 0, so as to 
make w negative. 

Phenomena of Recoil. 

Practically the phenomena are much more complex, since 
the rotation of the system is not immediate. 



Wheeled Carriages. 

In these the wheels tend to slide or rise to an extent 
determined by the resistance to sliding at T. Since T is 
not necessarily on a reciprocal axis of spontaneous rotation, 
the stock is subjected to a transverse stress. When, after 
rotation, the wheels fall, the axle receives a shock, and the 
trail being thrown up, the system recoils by roUing, and so 
on until the system comes to rest. 

Rotation during the first period tends to derange the aim 
by what is called the angle of jump^ See Chapter XX. 

During the first period, since the trunnions fit rather 
loosely in their beds, a frictional moment is developed on 
the under side of the trunnions This causes abnormal 
pressure on the head of the elevating screw, which, owing 
to the elasticity of the system, subsequently receives one or 
more severe blows from the breech. The effect is destructive, 
since the bearing of this screw upon its nut is restricted, and 
the necessary play between the screw and nut increases the 
striking velocity of the parts. 

The objections may be mitigated by making the piece 
without preponderance, and by arranging the elevating screw 
so that its axis will be always normal to the surface which it 



XXII. — ARTILLERY CARRIAGES. 



supports, since this will avoid the tendency to bend under 
pressure. 

Other phenomena also occur. 

The inertia of the wheels develops in the axle a consider- 
able transverse stress. 

In rifled pieces a rotary moment is developed which tends 
to raise from its bed the trunnion toward which the top of the 
projectile is revolving, and thus to raise one wheel higher 
than the other as the system jumps. The effect will be to 
concentrate most of the shock of the fall upon the lower 
wheel. 

Stationary Carriages. 

The chassis of stationary carriages revolves around a massive 
vertical pintle which may be placed in front of the chassis or 
at its middle. 

While the former position is necessary for pieces firing 
through embrasures, in other cases the center pintle chassis 
is preferred, since a given change in azimuth covers less 
ground. 

The tendency of the top carriage to jump is restrained by 
projections which engage under the chassis, but tend to lift 
the pintle from its socket. The pintle is also exposed to a 
horizontal stress nearly equal to the normal pressure between 
the carriage and the chassis multiplied by the sine of the 
inclination of the chassis to the horizon. 

The strength of the pintle and its fastenings is therefore an 
important subject of consideration. 

Angle of Greatest Recoil. 

Since the energy of recoil is distributed between the 
motions of rotation and translation, the maximum velocity 
of recoil will follow from an angle of fire such that w = 0. 
Equation (8) does not contain all the data necessary for a 



10 XXIi. — ARTILLERY CARRIAGES. 

full discussion ; but it may be shown that, if the weight of 
the system be neglected, and the notation of figure 2 be 
adopted, if we call the angle of greatest recoil, 6^, then 

Since A'^/i, this value of B^ is always positive, or the 
maximum velocity of recoil will follow the use of an angle 
of fire ]>0. This value of 6 should therefore be employed 
in all calculations relating to limiting the extent of recoil. 

The angle 6^, may also be called the ang/e of no rotation^ 
i. e. the angle for which all the energy of recoil is expended 
in translation only. It may be taken to measure the exposure 
of the system to the injurious shocks resulting from rotation, 
since, in ordin-ary firing, Q is less than Q^^ and therefore rota- 
tion is ordinarily produced. 

Equation 9 shows that d^ may be diminished by the fol- 
lowing means : 

1. By making h' — h as small as possible. Owing to the 
length of a in stationary carriages this correction is princi- 
pally confined to those that are wheeled. In these h' is 
made as small as facility of loading and the protection of the 
gunners by the parapet will permit, and h is increased by 
bringing the axle as near to the trunnions as the size, strength 
and weight of the wheel will allow. 

2. By making a as long as conditions relating to mobility 
in transportation will permit. , 

3. By making /small. 

In stationary carriages / is normally great, and, as here- 
after seen, the resistance to sliding is generally artificially in- 
creased. For these carriages it is especially necessary that a 
be made large. 

The stresses developed in field carriages by a large value 
of/, as when the site is sandy or the trail is rested against a 



XXII. — ARTILLERY CARRIAGES. 11 

rock, are evidently prejudicial. They may sometimes be in- 
evitable, as when firing across a valley at a high mark, since 
in such a case the trail may require sinking into a hole. 

DEVICES TO CONTROL RECOIL. 

These may be considered according to the end in view, 
as they seek, I, merely to limit the path; or, II, to regulate 
the resistance. 

It is generally advisable to store up enough of the work of 
recoil to assist in bringing the piece back into battery. The 
return may be facilitated by the use of eccentric rollers. 

These devices ar-e often combined in the same carriage. 

Class I. To the first class of devices belong those in which 
the energy is absorbed by friction or in which a weight is 
raised. 

Stationary Carriages. 
Friction Checks. 

This variety is least valuable since it stores up no useful 
work. In the best types the friction, due to the normal com- 
ponent of the weight, is increased by the artificial pressure 
of a screw clamp. 

The effect of a given pressure on the screw may be in- 
creased by increasing the number of surfaces upon which it 
acts. Thus, in Ericcson*s compressor we have 7i parallel plates 
attached to the chassis and alternating between n -\-l pieces 
so attached to the carriage that while they recoil with it, a 
sHght initial play is allowed. Suppose this play to be de- 
stroyed by a normal pressure P. We shall then have for the 
friction of the compressor P =: P/ {2 n) and from Equa- 
tion (7) 

(v cos 13 y 



2g(s[nf5+/cos(3+-^j 



(10) 



12 XXII. — ARTILLERY CARRIAGES. 

The main objection to this system is the variable value of 
F^ since this depends upon the judgment of the operator, and 
upon the state of the surfaces, and is greater for static friction, 
when the acceleration is greatest, than afterwards. 

This arrangement is modified in the Sinclair check used 
with some converted U. S. Sea Coast guns. 

This consists essentially of a clamp embracing a plate in- 
creasing slightly in thickness from front to rear. To prevent 
the plate from buckling in consequence of the counter recoil 
produced by the elasticity of the parts, the front end of the 
plate is free to move forward through its attachment to the 
chassis. 

Wheeled Carriages. 

These may be braked by various means. Among these is 
the Hotchkiss brake which consists of nuts threaded upon the 
axles between the wheels and serving, by friction produced 
against the hubs of the wheels, to keep the wheels from 
turning. 

This brake is an example of the friction clutch often em- 
ployed in the transfer of energy. When the tangential com- 
ponent of the force producing rotation exceeds that of fric- 
tion, sliding takes place and the destruction of the resisting 
parts is averted. 

This principle is sometimes applied to the elevating screw, 
since the clutch, which is required to vary d only, will 
yield under the shocks of recoil and save the deformation 
of the parts. 

A simple brake may be extemporized by lashing the 
wheels to the trail by a rope ; but, as this strains the wheel, 
a better way, often used, is to rest the wheels on shoes 
attached by tension to the trail, as in wagons of commerce. 

The latest patterns of brake admit of a partial distribution 
of the pressure, as explained later and in Chapter XXIII. 



XXII. ARTILLERY CARRIAGES. 13 



They may also be used in transportation without necessarily 
stopping the carriage, as is required when the shoe is used. 

Raising a Weight. 

If the piece raise its own weight, its exposure is increased ; 
while, if it raise a counterpoise, it may itself descend. Such 
carriages are called disappeari7ig carriages, 

Moncrieff Carriage. — Figure 3 

In this the flasks rock on the chassis so that the counter- 
poise, Wy which was at first beneath the gun, has finally 
a considerable moment of restitution. By varying the 
curvature of the flasks this moment may be made to vary 
inversely with the acceleration of the recoil so that the 
stresses between the piece and the counterpoise may be 
nearly constant. Conversely, the return to battery will be 
gentle. The rack and pinion serve to retain the piece for 
loading, and to control its return to battery. 

Kings Carriage. 

The chassis is steeply inclined to the rear, and the coun- 
terpoise, which is in a well, is lifted by a rope passing 
through the pintle. 

This carriage, invented by Major King of the Engineers, 
is cheaper than the Moncrieff", and has been successfully 
tried in the United States. 

In both carriages exposure may be minimized by aiming 
with mirrors, and by firing by an electrical contact automat- 
ically made when the piece comes into battery. 

• 
Regulation of Stress. 

1. BY FLUID PRESSURE. 

The method now generally adopted is the use of hydraulic 
or pneumatic buffers. 



14 XXII. — ARTILLERY CARRIAGES. 

These consist essentially of a cylinder and a piston, rela- 
tive motion between which results from the recoil. The 
effect is to force the fluid contained in the cylinder through 
orifices or ports which may be either constant or variable 
in size 

In the pneumatic buffer the ports are in the cylinder heads ; 
in the hydraulic buffer, as the liquid is to be used again, they 
are in the piston. 

Pneumatic Buffer, 

This, although simpler and requiring less attention than 
the hydraulic buffer, is more bulky, can be less easily regu- 
lated, and gives an injurious counter recoil. 

Hydraulic Buffer, 

Description. Let the arrangement be in principle such 
as shown in figure 4. C is the cyUnder filled with a non- 
freezing mixture of glycerine and water ; it is attached to the 
carriage P is the piston fixed on the rod R^ which is secured 
to the chassis. 

Many alternative arrangements are made. 

By placing it under tensile stress during the recoil, the 
bending of the rod may be avoided. 

The size of the ports in the piston may be varied by the 
profile of the ribs, r, which are fixed to the interior of the 
cylinder, or by a notched disc revolving on the piston and 
provided with projections which enter rifle grooves in the 
cyhnder. 

We will consider only the second period of recoil, and will 
neglect the friction of the liquid and that of the rod in its 
stuffing box, so that the pressure considered "^ill be that 
required to give a constant acceleration to the fluid. 

The value of this method appears from the fact that it may 
safely restrict the most powerful cannon to a recoil of about 
3 calibers. 

\ 



XXn. — ARTILLERY CARRIAGES. 15 



Notation, , 

Let: 

A be the area of cross-section of the bore of the cylinder 
diminished by that of the piston rod and ribs. 

a^ the total initial area of the ports. 

a this area at the end of the time, /, or after a displace- 
ment, X. 

v' the corresponding velocity of the liquid current. 

11 the corresponding velocity of recoil. 

Vq the initial velocity of recoil, obtained either by meas- 
urement or by means of the formula 



("'+?) 



.„- ^_ r;[cos(e, + /3)-/sin(9, + /3)] (11) 

derived from Equation (9), Chapter VII, and the remarks 
noted on pages 7 and 10 herein. 

6 the density of Uquid, or the ttiass of one unit of its 
volume. 

P the pressure on the piston at any moment. 

a the corresponding acceleration. 

Extent of recoil. If the cylinder is full, the volume a v', 
of liquid which in a unit of time passes from in front of the 
piston to the rear must be equal to the volume, A u caused 
by the translation of the cylinder, whence 







Au 








(12) 


The 


mass of the 


liquid 


escaping in 


the 


time 


A/ 


is then 




;;/ = 


8av' 


A/= 6 A u 


A/ 






(13) 


and its 


energy 


mv"' 


6 A' u'/\ t 


- 






a4) 




2 


- 2d' 



16 XXII. — ARTILLERY CARRIAGES. 



This is equal to the work done by P over the path u A /, 
and therefore 

„ d A" u^ 

Since P is constant, Equation (15) must be true, for the 
initial values of u and a, and therefore 

From this, by equating the initial energy of the system, 
with the work of the resistances, including the lifting of the 
weight of the system, and the work of friction over the path 
iS", we have 

~\^^^\_~2^' +^-^s(sin/3+/cos/?)J, (17) 

from which S can be determined when A and a^ are known, 
or from which a^ can be determined when *S and A are 
known. 

Profile oj the ribs. From the theory of energy we have 

or 

u=K^l-^-^ (19) 

Also, since the recoil is uniformly retarded if we consider 
the resistance of the liquid only, we have 

Fl = 2a S 
which value of VI in Equation (19) gives 



«=K\/i-i- 



which from Equations (15.16) may be written 



-V^ 



(20) 



(21) 



XXII. — ARTILLERY CARRIAGES. 17 



a 
If there are n similar ports, the area of each one is - -. If 

n 

each notch in the piston has a breadth, b^ and a depth, d^ 

and the rib has the same breadth and, as shown by figure 4, 

a variable depth, j, then 

a = nb {d — y) (22) 

Which value of a substituted in Equation (21) and solved 
with respect to y gives 

This is the equation of a parabola. 

At the end of the recoil, when x = S, y =z d, or the ports 
are completely closed 

This formula applies only to the path of the recoil after 
the system has acquired its maximum velocity or during the 
second period. 

While the projectile is in the gun the piece recoils from one 
to two inches and continues to gain velocity for four to six 
inches more so that the maximum velocity is not attained 
until after a recoil of five to eight inches 

Figure 11 shows these phenomena and the effects of a 
suitable control, based largely upon the analysis of velocity 
curves obtained during the practically free recoil of the ])iece. 
The data were as follows : Weight of piece, about 100000 
lbs. ; of projectile, 754 lbs. ; of powder, 244 lbs. ; initial 
velocity, 1857 f. s. 

Cylinder, The thickness of the walls of the cylinder may 
be determined from Equation (4), Chapter XIX, by placing 






The area A will be determined practically by the construc- 
tion of the chassis. As the depth of the chassis limits the 



18 XXII. — ARTILLERY CARRIAGES. 

diameter, it is customary to have two cylinders connected by 
a tube so as to equalize the resistances and prevent slueing. 

Counter RecoiL Owing to the incompressibility of most 
liquids the tendency to counter recoil is slight ; and, as the 
velocity of return is small, the weight of the system generally 
suffices to return it to battery. 

Or the hquid may be forced into another vessel or a set of 
stationary vessels containing air or powerful springs, which 
store up energy to return the piece to battery when a valve 
or latch is opened. Figure 5 illustrates the operation of such 
a carriage. When air is compressed by the liquid, the variety 
is known as the hydro-pneumatic 

Regulation of Stress. 

2 BY THE ELASTICITY OF SOLIDS. 

The weight of the cylinder, and the difficulty of prevent- 
ing leaks in the preceding apparatus, renders it objectionable 
in wheeled carriages, and more so for those used in the field 
service than for those in the siege service 

A compromise has therefore been sought by the inter- 
position of an elastic solid, the work done upon which in the 
first period will reduce the shock felt by the system. The 
restoration of this work is not essential, although it tends to 
distribute the stresses over the path. 

Such an arrangement is shown in the Engelhardt (Russian) 
carriage, figure 6. 

Engelhardt Buffer. The flasks are notched so as to allow 
the axle, a^ a limited play. They are also similarly pierced 
for the cross-bar, ^, each end of which is united to the outer 
end of «, by a brace, k. This keeps the axle from bending 
easily since the force of recoil is applied close to the wheels. 

The transom, c^ separates e from an elastic buffer, K The 
buffer consists of layers of cork, rubber, or of Belleville 



XXII. — ARTILLERY CARRIAGES. 19 



Springs {post ), assembled on a bolt, /, the front end of which 
is secured to e, and the rear end of which is provided with a 
nut, d. 

When discharged, the piece, with its flasks and c and b, 
slides back relatively to the wheels and / and ^, so that b is 
compressed. A considerable proportion of the energy of re- 
coil is thus absorbed before the wheels begin sensibly to move. 

After recoil, the elasticity of b restores the parts. 

Belleville Springs, These are saucer shaped discs of sheet 
steel, pierced by an axial hole by which they are united in 
pairs on a spindle, base to base. They are now much used 
under compression where space is limited. 

Lejnoine Brake. The French artillery have borrowed from 
the omnibus of Paris a more perfect but more complex brake, 
figure 12. On the march it may be set against the tire, by 
hand, as in the wagons of commerce. When the piece is 
fired, the relative motion of a mass, w, throws forward the 
elastic cross-bar, b^ to each end of which is attached a taper- 
ing cord, c. Each cord after making several loose turns 
around the nave is secured to the brake beam, B. When m 
is thrown forward it is held in place by the serrated edge of 
an axial bar, b', to which it is secured. The motion of b 
stretches the cords and tightens them around the naves so 
that they are further wound up by the revolution of the 
wheel in recoiling. 

The greater the extent of the recoil at any instant, and 
therefore the less the velocity of recoil, the thicker will be 
the cord and therefore the greater will be the increment of 
the pressure of the brake upon the tire. 

See also the U. S. Buffington brake in the next chapter. 

PLATFORMS. 

To insure continued accuracy of fire from the same site, 
it is absolutely necessary that the carriage should rest upon 
a solid and substantial platform, 



20 XXII. ARTILLERY CARRIAGES. 

The mobility of field pieces restricts this necessity to the 
sea coast and siege services. 

In the sea coast service the platforms are constructed by 
the Engineer Department with the works which the cannon 
defend. 

Wooden platforms are employed for siege pieces, in which 
long continued firing at one object as in breaching, would 
cut into the unprotected soil deep ruts, which would increase 
the difficulty of serving the piece and restrict both its 
horizontal and vertical field of fire. 

The construction of the platform should be such that it 
may be taken up without injury for removal to another site. 

Siege platforms consist of a certain number of pieces of 
wood ; and in order that these pieces may be carried on the 
backs of soldiers from the depot to the battery, the weight 
of the heaviest piece should not exceed fifty pounds. Siege- 
platforms consist of sleepers (i), (fig. 7), and deck platik (2). 
The general direction of the sleepers is parallel to the axis 
of the piece, and the deck-plank at right angles to it ; this 
disposition of the parts offers the greatest resistance to the 
recoil of the carriage. The deck-planks are fastened together 
at their edges by dowels ; the outer planks are secured by 
iron eye-pins, one at each end of a sleeper. The platform is 
secured in its place by driving stakes around the edges. 

There are two principal platforms for the siege-service, viz., 
the ^2^;z-platform and the mortar-'^XdXioxm. The former is 
composed of twelve sleepers and thirty-six deck-planks; the 
mortar-platform of six sleepers and eighteen deck-planks. 

A simple and strong mortar-platform, called the rail- 
platform may be used where trees or timber can be easily 
procured. This is composed of three sleepers and two rails, 
secured by driving stakes at the angles and at the rear ends 
of the rails. The rails are placed at the proper distance 
apart to support the cheeks of the bed. 



XXII. — ARTILLERY CARRIAGES. 21 

II. TRANSPORTATION. 

For certain light pieces, as machine guns, a two-wheeled 
vehicle is used. Where the weight of the load requires its 
distribution on several supports, the gun carriage is converted 
into a four-wheeled carriage by attaching it to another two- 
wheeled carriage, called the limber. 

PRINCIPLES OF THE WHEEL. 

In transportation the wheel is intended to transfer sliding 
friction from between the surfaces of the tire and the ground, 
where the coefficient of friction is large and variable, to the 
lubricated surfaces of an axle and its bearing, where the 
coefficient is small and nearly constant. 

In this respect its value as a mechanical power varies 
directly with the radius of the wheel and inversely with that 
of the bearing. 

The wheel, as shown by figure 8, increases also the lever 
arm, /, of the power, P, with respect to that, q, of the weight, 
W^ to be raised over the obstacle, h. 

On these accounts, since the diameter of the bearing, 
which is generally equal to that of the axle arm, is fixed by 
the maximum stress which the axle arm has to support, the 
mechanical advantage of the wheel increases with its diameter. 

An increase in diameter as well as in the width of the tire, 
diminishes the pressure per unit of area between the tire and 
the ground, and therefore diminishes the rolling friction, or 
the work lost in permanently deforming the ground on which 
it travels. The elasticity of the wheel also favors this reduc- 
tion ; hence the use for railways of iron wheels on iron 
tracks. 

The increase in size is limited by the weight of the wheel, 
the stability of the system on the march and in firing, and the 
convenience of loading. The mobility of transportation 
also limits the size, for all wheels in the same service being 



22 XXII. — ARTILLERY CARRIAGES. 



interchangeable, the facility of turning depends upon their 
diameter, as will be shown. 

As shown by figure 8, an advantage also follows from 
inclining the direction of the draught, particularly for the 
front wheels, which do most of the work of rolling friction 
and which therefore are designed to carry only about J of 
the total load. Since the point at which the horse exerts his 
power is fixed by his conformation, it is evident that this 
advantage will be diminished with the increase of diameter of 
the wheel. 

These considerations have generally fixed the diameter of 
all field artillery wheels at about 5 feet, and their weight at 
about 200 pounds. 

Siege wheels are made heavier and larger. 



CONSTRUCTION OF THE WHEEL, 

The requisites of size, weight, elasticity and facility o. re- 
pair demand a more general use of wood in the wheel than in 
other parts of the carriage, and involve a marked application 
of the principle of independence of function. This will ap- 
pear by comparing the rudimentary wheel, still used in remote 
districts, consisting of a disc cut from the trunk of a tree, with 
the complex elastic structure employed in the bicycle. 

The Archibald wheel, figure 9, now much used in the U. S., 
resembles that now generally employed in other services, 
although it applies less fully the principle above named. 

Starting from the center, which is the best way of consid- 
ering any circular structure, we find : — N^ N\ the 7iave or 
hub. This receives the pressure of the axle arm on a lubricated 
surface, and distributes the pressure to the spokes. The nave 
is made in two parts, to facilitate repairing the spokes. The 
portion of the nave in contact with the axle, or the axle box, 
is so shaped as to receive the lubricant in the cavity, O, 



XXII. ARTILLERY CARRIAGES. 23 

In some foreign wheels and in the ordinary wooden wheel 
the axle box consists of a separate piece, so that it may be 
replaced when worn. Since friction is less between dissimilar 
metals than between surfaces of the same metal, and in order 
to cause the wear to take place most on the part which can 
be most easily replaced,* the axle box, when separate, is pref- 
erably made of phosphor-bronze, while the nave, as in the 
Archibald wheel, may be made of malleable cast iron. The 
metal nave marks a great improvement over the wooden nave 
formerly employed. The cross section of this piece made it 
difficult to season, its softness caused it to wear from the 
alternate compression of the vertical and extension of the 
horizontal spokes, and it was especially exposed to decay 
from moisture lodging in the angles between the spokes. 

6", 6", are the spokes, which transmit the weight to the rim. 
For elasticity and facility of repair they are made of oak or 
hickory. Their inner extremities are shaped like voussoirs, 
which abut closely upon the box to avoid destructive play. 
In the Archibald wheel the voussoirs are made a trifle large 
and simultaneously set together by a powerful radial press 
which subjects them to a stress many times greater than they 
are likely to receive in service. 

R is the rmi which distributes the weight over the ground. 
For the same reasons as the spokes, and because mud adheres 
less to wood than to iron, the rim is made of oak. In order 
to avoid cutting too much across the grain the rim consists 
of a number of segments called felloes or fellies. 

T is the tire, shrunk on to bind the parts together and to 
protect the rim from wear. As it may require shortening in 
order to produce the necessary compression on parts which 
have become loose from wear, it is usually made of wrought 
iron or of low steel. 

*This is an important principle in machine design. 



24 XXII. — ARTILLKRY CARRIAGES. 



The figure shows also various bolts and clips and the 
line h pin and ivasher, the functions of which are evident. 



Dish. 

The spokes are so arranged as to form a conical surface 
which is called ih^dish. The principal object of the dish is 
to give stiffness to the wheel, since (figure 13) on a trans- 
verse slope or on uneven ground, the lower wheel, which 
bears the greatest share of the weight, will resist the lateral 
thrust of the axle by a compressive stress upon the spoke. 
If the spokes lay in the plane of the rim, there would be an 
alternating transverse stress on the ends of the spokes ; this 
stress would make them work loose in their sockets and accel- 
erate the destruction of the entire machine. 

Axle. 

T\ie axle or axle tree consists of the body and the arms. 
The arms are conical so as to give the greatest strength with 
the least mean diameter. In some vehicles, the wear between 
the arm and box is taken up by means of washers of varying 
thickness. 

The axis of the arm is inclined slightly downward, forming 
the hollow^ and to the front, forming the lead. Both together 
constitute the set of the arm. 

In a dished wheel the hollow frees from transverse stress 
the *' working spoke," which is that which bears the greatest 
load ; it also relieves the linch pin from thrust. For a given 
width of carriage body it allows the axle body to be made 
shorter and therefore stronger ; and, from the inclination of 
the plane of the rim, it tends to throw the mud clear of the 
carriage. 

The efiect of the lead is to diminish the transverse stress 
upon the front spoke in meeting obstacles. 



XXII. — ARTILLERY CARRIAGES. 25 

Axle Body. 
Although the interval between the cheeks transfers the 
transverse stress upon the axle to points near the wheels, it 
was found necessary in former carriages to reinforce the axe 
with a wooden body. In modern carriages this is sometimes' 
replaced with two grooved plates which clamp the cylindrical 
axle between them and are extended to the front and rear so 
as to stiffen the axle in recoihng. They also serve to fasten 
the axle to the cheeks. The axle may, without sensible loss 
of strength, be made hollow, and three-fourths of its weight 
when solid. 

THE STOCK. 

The prolongation of the cheeks is called the stock. The 
use of metal instead of wood, has permitted a return to the 
construction of the great French designer. General Gribeau- 
valy in whose gun carriages the flasks were parallel extensions 
of the cheeks. 

The metallic flasks now used converge to the trail. 

In the stock trail syste?n, recently in use, the cheeks con- 
tained between them a single piece of wood called the stock. 

Besides its functions under fire the stock of the gun carriage 
unites the two axles of the four-wheeled vehicle, as does the 
reach or perch of the ordinary vehicle. For artillery carriages 
used simply for transportation, such as the caisson and the 
forge, the stock is a single piece of wood joining the body to 
the limber. 

Tiirnmg A?igle. 

The dimensions of the stock affect the mobility in turning. 
This is often measured by the tiirfiing angle, which is half the 
horizontal angle through which the pole can revolve when 
the carriage is at rest. Practically, the space required to turn 
the carriage will vary with : 

1. The length and width of the line of horses and their 
gait. 



26 XXII. — ARTILLERY CARRIAGES. 

2. The distance of the pintle from the vertical plane tan- 

gent to the rear face of the front wheels. 

3, The thickness of the stock at the point rubbed b" the 

wheels in turning. 
• 4. The length of the stock. 

Owing to the first condition above named a turning angle 
of 60° is generally considered as sufficient. This may be 
increased by increasing the distance of the pintle from the 
front axle, but this is apt to cause the pole to *' thrash." 

Pintle. 

The distance of the pintle in rear of the axle in connection 
with the moment of the trail, afiects also the pressure on the 
necks of the wheel horses caused by the moment of the pole. 

In siege carriages and in those used only for draught, the 
pintle is placed at some distance to the rear ; or a similarly 
placed transverse sweep bar is used, which supports the 
weight of the stock. 

But, in field carriages for which flexibility of attachment 
and mobility are essential, the pintle is placed more to the 
front and the evil corrected as far as possible by distributing 
the load or by various mechanical means. 

In this arrangement the preponderance of the system com- 
posed of the gun and its carriage is an important factor. If 
the trunnion beds are moved towards the Hmber the pole is 
lifted, but the labor of Hmbering is increased, and the sta- 
bility of the carriage in firing is diminished. (Eq. 9.) 

To diminish the labor of limbering, the pintle is placed as 
low as permitted by the requirement that as much free space 
as possible should be left beneath the axles for mobility on 
ground covered with large stones, stumps, etc. 

In the siege service, as the piece does not require to be 
brought into action rapidly, and as the limber carries no 
extra load, the piece may be shifted to the traveling trunnion 



XXII. — ARTILLERY CARRIAGES. 27 

beds which, on the march, are in front of those from which 
the piece is fired. 

THE LIMBER. 

Nomenclature. 

The wooden field Umber, figure 10, is composed of an 
axle tree (1) ; a fork (2) ; two hounds (3, 3) ; a splinter bar 
(4) ; two foot boards (5, 5) ; a pole (6) ; the pintle hook and 
key (7); two pole yokes (8, 8); and pole pad {^). 

Ahhough destined to be soon replaced by one composed 
more largely of steel, it is here discussed as it illustrates some 
valuable principles- 

The hounds serve to support the ends of the limber chest 
and the foot boards, and also to transmit the draught of the 
horses from the splinter bar to the axle. 

The pole or totigue is employed to stop the carriage and to 
give it direction. As it is liable to be broken, it is practically 
made in two pieces, of which the fork, which is least exposed 
to accident, forms one. The fork then is a socket for the 
pole, and braces the entire frame by its attachment to the 
axle body and the parts in front. 

The pole should be so attached to the fork that it may be 
readily replaced when broken. 

The pole yokes transfer the weight of the free end of the 
pole to the necks of the wheel horses and the soft pad pro- 
tects the leading horses from harm. 

Attachments, 

The metaUic limber body consists of channel irons and T 
angle irons united in various ingenious ways. The rigid 
splinter bar may be replaced by the ordinary jointed double 
tree and si?tgle trees. These permit the horses to work more 
independently of each other than the splinter bar does, but 
are probably not so strong. A joint is always a cause of 
expense and generally a source of weakness. 



28 XXII. — ARTILLERY CARRIAGES. 

In the British service the pole is replaced by shafts. 
Since the pace of the team is regulated by that of the slowest 
horse, this arrangement, while more manageable than the 
pole, and therefore better fitted for the showy evolutions of a 
drill, is objectionable for the march, since the work which 
devolves on the shaft horse diminishes his endurance. 

The Limber Chest 

This serves to carry ammunition, and also furnishes a seat 
for some of the cannoneers. The gun carriage is often 
arranged to carry two cannoneers on side seats, in order to 
diminish the time required for coming into action, a matter 
which, owing to the precision, rapidity and range of infantry 
fire, is becoming of vital importance. The carriage also 
often carries two rounds of canister for use at close quarters. 

The principal distinction between limber chests depends 
upon how the lids are placed. 

If on top, the chest may easily be made waterproof in 
fording streams ; but the contents are less accessible. If 
behind, the lid may form a convenient tray for preparing 
fuzes, &c. This arrangement is more liable to accidental 
opening than the former, and waterproof packages for the 
cartridges may be necessary. 

The ammunition chests in the U. S. Service are still con- 
structed of wood. In other countries sheet steel is generally 
used. For what reason is unknown ; since, if not unduly 
heavy, they are not proof against infantry fire. 

THE MORTAR WAGON. 

This is used for transporting siege projectiles, mortars and 
their beds, and spare guns. 

The body consists of a strong, rectangular frame provided 
with a stock by which it is attached to the siege limber. At 
the rear of the body is placed a windlass which aids in loading 



XXII. ^ARTILLERY CARRIAGES. 29 

heavy weights. Stakes may be placed around the sides to 
sustain boards used in retaining loose objects. 

Since rifle projectiles are always issued boxed instead of 
loose, as was the former custom, the necessity of the mortar 
wagon for their transportation no longer exists; but its 
general utility is great. It will .probably be used hereafter 
for transporting siege guns for considerable distances, since 
the height of the carriage from which they are now fired 
renders them unstable on rough roads. 

A special wagon with a crank axle, so arranged as to carry 
the load close to the ground without diminishing the height 
of the wheels would appear to offer special advantages. 

III. CARRIAGES FOR SUPPLY. 

New U. S. System. 

These include, 1st, the caisson^ for carrying a larger quan- 
tity of ammunition than can be carried by the limber, and 
also a spare pole, wheel, handspikes, buckets and tools ; 
2nd, the forge and battery wagon, containing a larger assort- 
ment of tools and material for repairs ; 3rd, the artillery 
store wagon, an ordinary four-horse wagon, containing extra 
small arms and ammunition and the men's knapsacks, etc., 
so as to confine the load of the fighting teams to the neces- 
sities of action. 

REMARK. 

The increased weight of each round of modern ammuni- 
tion and the necessity for an even greater number of rounds 
than formerly sufficed, increases the difficulty of supply. 

It is proposed abroad to increase the number of caissons 
per piece and to retain the supply in the limber for extreme 
emergencies. 



XXtil. — VARIOUS AkTiLLEkY CaRria6E§. 



CHAPTER XXIII. 
VARIOUS ARTILLERY CARRIAGES. 

The U. S. Field Carriage. Figures 1-4. 

Constmction, 

This carriage, designed by Colonel Buffington of the Ord- 
nance Department, is made of steel, since, owing to the large 
value Qii h of this gun (Chapter XI, page 21), wooden car- 
riages, and even some differently constructed of steel, were 
found insufficiently strong. 

The principal features relate to the construction of the axle 
body, of the stock and to the operation of the brake. The 
hollow cylindrical axle is strengthened by axle plates, figure 
2, which stiffen it in the direction of the recoil. The stock 
consists of two brackets, each of which is made of two nearly 
symmetrical sheets of steel stamped hot between dies so as to 
give the corrugated cross section indicated in figure 3. When 
riveted through the webs, each bracket forms a strong, light 
truss, resisting stress both in its own plane and transversely. 

The lower flanges of the outer plates project inwardly and 
serve to unite the brackets to the axle plates. The brackets 
are further united by transoms, three of which with a hinged 
lid form the trail box for the oil can and tools which have 
become a necessary portion of the equipment. 

The carriage is provided with two axle seats for cannoneers. 

The wooden handspike is permanently hinged to the trail. 

Elevating Screw, 

The space between the brackets allows the breech to 
descend sufficiently for the high angles of fire used with low 



XXIII. — VARIOUS ARTILLERY CARRIAGES. 



charges against troops sheltered, from view, and the crank 
which operates the elevating screw is placed at the side, so 
that under these conditions it will be readily accessible. 

The nut of the elevating screw oscillates slightly on trun- 
nions, and the head of the screw is connected by a fork to 
an axis parallel to and beneath the trunnions, so that, as the 
angle of fire changes, the axis of the screw will be nearly 
normal to that of the gun. 

Brake. 

The great strength of this carriage has permitted the 
employment of Colonel Buffington's brake, figure 4. 

This consists of an [_ shaped rod, the stem of which is 
surrounded by a spiral spring contained within a tube ; the 
rod swings freely from a loose joint situated eccentrically 
above the axle. 

The length of the brake is such that when held vertically 
the hook will pass over the wheel ; and, being allowed to fall 
to the rear, it will engage with the tire at some point as a. 

When the wheel revolves in the recoil, the friction at a 
tends to extend the rod. But this compresses the spring and 
increases friction, so that as the velocity of recoil decreases, 
the resistance to rolling increases, and the retardation 
a])proaches constancy, at least during the critical period 
preceding sliding. 

The recoil has thus been reduced from 26 feet to 8 feet, 
without injury to the carriage. 

In transportation the brake is secured vertically to one of 
the seat arms. It may also be used as a traveUng brake. 

Limber and Caisson. 
These carriages are constructed substantially on the lines 
previously named. Steel angle irons are largely used for the 
frame. 



XXIII. — VARI6US ARTILLERY CARRIAGES. 3 

The chests, which are of wood, open on top and are only 
high enough to receive the projectile standing ; this brings 
the center of gravity very low. 

The cartridges lie in a compartment between the two end 
compartments reserved for the projectiles, which thus serve 
to protect the powder from hostile fire. 

For safety, no friction primers are carried with the powder, 
as was formerly done. Unbroken packages are placed in 
outside cases, and loose primers are carried with the tube 
pouch in the trail box. 

The four chests per piece can carry 42 projectiles each, 
with a greater number of cartridges for curved fire. 

The Siege Carriage. Figure 5. 

The principal feature of this carriage is its height. For 
the protection of the gunners the axis of the trunnions is 
placed 6 feet above the ground. 

In order to prevent the system from tipping forward in 
limbering, the trunnions are so placed that when limbered 
the center of gravity of the system will fall between the axles. 

The wheels, axle plates and brakes are such as just 
described. 

The carriage is intended to transport the piece only for 
short distances about the work which it defends. 

REMARK. 

A small hydraulic buffer connecting the stock with a pintle 
sunk into the platform between the wheels, and two movable 
chocks, assist in controling the recoil. The chocks rotate 
around the pintle with the gun and serve to return the piece 
into battery. 

The Siege Howitzer Carriage. Figure 6. 

The piece is mounted in two trunnion carriages, a, upon 
the inclined slides, '^, upon which it is allowed a recoil of six 



4 XXIII. — VARIOUS ARTILLERY CARRIAGES. 

inches. The recoil upon the shdes is checked by the 
hydrauhc cyUnders, r, and the courses of Belleville springs, 
d. The latter serve to return the piece to the firing position. 
They rest against the traveling trunnion beds, e^ and the rods 
upon which they are strung pass through holes in these beds. 

The flasks, /, are of rolled steel plate \ inch thick, and are 
flanged inward except on their upper edges. From each 
flask is cut a large triangular piece in order to diminish its 
weight ; the edges of the apertures being flanged inward as 
above. The flasks are xmited by three transoms, ^, and the 
double transom, //, to which is fastened the piston rod of the 
hydraulic brake. 

The flasks rest upon the axle through two iron forgings, /, 
and are strengthened by two supporting plates,/. 

In order to facilitate the elevation of the piece a pecuhar 
arrangement is employed. This consists of the elevating 
rack, /, which is attached to the piece, and the worm, m ; the 
shaft, ;/, and the hand-wheel, o. The worm is attached to 
the right trunnion carriage, and in recoihng slides along the 
shaft, n. A spline (see AVebster) on the shaft permits the 
worm to shde along the shaft, and yet constrains it to follow 
in any position the rotation given to the hand-wheel, o. 

The advantage claimed from this design is that the recoil 
of the piece upon the carriage so diminishes the maximum 
stress upon the flasks and trail that their weight may be 
greatly reduced. A portion of the weight so saved is used 
to strengthen the axle and the wheels. 

Weight of wheels, 375 pounds, each. 
Weight of carriage, complete, 3200 pounds. 
Pressure of trail on platform, 13(K) pounds. 
Height of trunnions, 6 feet. 



XXIII. — VARIOUS ARTILLERY CARRIAGES. 5 

Barbette Sea Coast Carriage.* 

The principal feature of the gun carriage is borrowed from 
the old *' flank-defense howitzer" carriage. 

Its object is to return the piece to battery and by diminish- 
ing the variable work of sliding friction to increase that of 
the hydraulic buffer, which can be made constant. 

Each cheek carries two rollers ; that in rear is on an 
eccentric axle and that in front is on a concentric axle. 
When the piece is in battery the front rollers are nearly in 
contact with the chassis rail ; while those in rear are usually 
raised from it, but may be thrown in contact by means of the 
eccentric. The lower front angles of the cheeks are trun- 
cated, so that, when the carriage is thus tilted to the front, all 
the rollers come into play and the piece may be moved from 
battery with comparative ease. 

In firing, the rear rollers are out of gear so that the vertical 
thrust of recoil is borne by the lower face of the cheek and 
the axles are not endangered. 

As the carriage recoils the rear rollers strike inclined planes 
bolted to the upper surface of the chassis rails and tilt the 
carriage sufficiently to cause it to move by rolling until it 
returns again to battery. 

Muzzle-loading guns are retained from battery by means of 
an automatic latch. 

MODERN TYPES OF SEA COAST CARRIAGES. 

Owing to our deficiency in modern cannon the U. S. have 
not yet (1891) decided on any special pattern of sea coast 
carriage; but the following examples, derived from the 
French service, probably contain the essential features of the 
system to be adopted for the barbette carriages, as soon as 
the new cannon shall have been supplied. 

* The Sea Coast Battery at West Point contains several specimens of 
this type. 



O XXIII. — VARIOUS ARTILLERY CARRIAGES. 

The types of disappearing carriages and those designed 
for turrets are too numerous for description here. They 
generally apply the principles previously discussed with those 
treated in the course of Military Engineering. 

Gun Carriage. 

Figures 7, 8 represent the elements of a modern sea coast 
barbette gun carriage. It consists of three main parts : 1st, 
the top carriage, T^ consisting essentially of the buffer; 2nd, 
the chassis, C, the lower part of which is circular ; by means of 
a great number of loose conical rollers, it revolves upon the 
circular pintle platform, P. This platform, cast in a single 
piece, rests upon a proper foundation. 

To avoid the complications due to sliding friction during 
recoil, the top carriage also moves on rollers recessed in the 
chassis rail. 

Pointing in azimuth is performed by an endless chain 
engaging in a sprocket* bed around the platform. The chain 
passes over a windlass, W, which is rotated by the crank, K, 

The loading scoop, s, is on a lever, L, which is rotated by 
a geared crank so as to bring both the charge and the pro- 
jectile into the position of loading. 

In order to minimize the number of men required for 
loading, the act of lowering the scoop stores up energy in 
certain springs so that the maximum pressure which can be 
counted on shall be continuously apphed, as in the hydraulic 
buffer. 

The steel shield, /, protects the gunners from light pro- 
jectiles. 

Advantages, The carriage is low, stable, and as seen in 
figure 9, very compact. The use of rollers increases its 
mobility and their number distributes the thrust over a large 
area. All wheels are protected and the traversing chain is of 



* See Webster. 



XXIII. — VARIOUS ARTILLERY CARRIAGES. 7 

rustic simplicity and easy of repair, even in action. The 
arrangement of the scoop facilitates loading since its load 
may be placed by simply tilting the hand truck on which it 
is brought from the magazine. 

Sea Coast Mortar Carriages. Figures 10, 11. 

Although of an entirely novel design, the carriage in figure 
10 resembles essentially the gun carriage just described. The 
nomenclature is the same in both figures. 

The chassis is divided into two portions, Ci, C^ ; the sur- 
face of contact being cylindrical about the axis of the trun- 
nions. By this arrangement fon all angles of fire the axis of 
the gun is always in the plane of the axes of the hydraulic 
cylinders, so that the friction in starting is not increased by 
the pressure causing recoil. 

Rotation from recoil is prevented by the clips, c, c, etc. 

The diminished intensity of the maximum vertical pressure 
has caused this carriage to be adopted in the French Navy; 
for ships now, as well as forts, are beginning to utilize the 
advantages of vertical fire. 

In another type of mortar carriage, shown in figure 11, also 
under trial in the U. S., the chassis is made in one piece, the 
direction of the recoil being downward at a constant angle of 
60° This is a mean between the limiting angles of 6 for 
mortar fire, viz. : 45" and 75°. The mortar is returned to 
battery by springs that are compressed during the recoil. 

Another form of loading scoop is also shown. 

This is known as the Easton- Anderson carriage, of Eng- 
lish design. 



XXIV. — H0RS£ AND HARNESS. 



CHAPTER XXIV. 

HORSE AND HARNESS. 

The horse transports his load in two ways. 1st, as a pack 
horse ; 2nd, as a draught horse. 

PACK HORSE. 

The daily work of a pack horse is about equal to that of 
five men similarly employed ; or, if he moves at a walk, he 
may carry a load of 200 pounds 25 miles a day, or 5000 mile- 
pounds. 

If he trots, the increased expenditure of muscular energy 
reduces his daily work about one-third.* 

In the above the weight of the horse is neglected, and it is 
assumed that, though this daily work may be temporarily ex- 
ceeded, the excess cannot be long continued without injury. 

The mule, owing to his build, carries more than the horse ; 
he eats less and is surer of foot. He is therefore generally 
used in the mountain service. 

DRAUGHT HORSE. 

Load. 

Although a horse can pull much less than he can carry, 
the advantages of the wheel enable him to draw over ordinary 
roads a load weighing about seven times as much as his pack. 
With a pull of 80 pounds the daily work of a draught horse 



* It has been found that for any animal the maximum rate of work per 
unit of time (or/ z/, Chapter XI, page 4) is attained when the velocity is 
about I of the maximum velocity unloaded, and the load about g of the 
maximum load at the lowest positive velocity. 



XXIV. — HORSE AND HARNESS. 



is generally given as 1600 pounds X 23 miles, or 36800 mile- 
pounds of load, or 1840 mile-pounds of actual work. 

Owing to their interference with each other's motions, the 
maximum load drawn by teams of horses increases less rapidly 
than does the number of horses in draught. Thus, when the 
teams comprise respectively 2, 4, 6, 8 horses, the maximum 
loads which they can continuously draw are in the relation 
per team, of the numbers 9, 8, 7, 6. 

These considerations, the mobility of the system (Chapter 
XXII, page 1), the increased weight of forage and length of 
column required, have generally fixed the limit of efficiency 
at the six-horse team. 

It is estimated that when a draught horse carries a rider, 
his efficiency is diminished J at a walk and § at a trot. Con- 
sequently, supplying the data given, the maximum load for a 
team of 6 horses moving at a trot will be about 



near files. off files. 

3 X 1600 3 X 1600 
+ ^ 



^1 = 3733 pounds; 



or 622 pounds per horse. 

This may be considered 2i physical constant^ the best method 
of distributing which between the objects transported and the 
means of transportation is still open to inquiry. 

Various conditions must be allowed for : On one hand are 
bad roads, insufficient food, rapid movements for short times, 
and forced marches. On the other hand, the reduction in 
the load caused by the expenditure of ammunition, the dis- 
mounting of the cannoneers, and the infrequency of the trot. 

Upon these considerations are based the following approx- 
imate loads per horse. 

Horse artillery, 650 pounds. 

Light field artillery, 700 pounds. 

Heavy field artillery, 850 pounds. 

Siege artillery, 1000 pounds. 



XXIV. — HORSE AND HARNESS. 



REMARK. 

The 12 pdr. Napoleon gun, which was the heaviest field 
gun used in our civil war, and which traveled over roads quite 
as bad as any used in foreign wars, gave a load of 645 pounds 
per horse, and was found amply mobile. The load per horse 
for the 3.2 inch B. L. R., field, is 632 pounds. 

Angle of Draught. 

The power of an animal in draught may be supposed to 
consist in his ability to maintain himself rigidly in a position 
such that the moment of his weight may be increased without 
increasing the lever arm of the resistance. 

Thus in figure 1, let / be the position on the ground line, 
/ g, of the hind feet of the horse in draught. Let s be the 
shoulder of the horse or the point at which he applies his 
power to the trace, s c, which is attached to the carriage at 
the point c. Let W be the weight of the horse, and / be 
the distance from / on the line / s, of the vertical passing 
through his center of gravity. Let r be the tension on the 
trace, the length of which s c ■=. t^ and let R be the horizontal 
component of r, producing uniform motion of the point c in 
a horizontal plane. 

Let / be the variable angle with the ground line of the line 
s /, and g} be the variable angle between s f and s c. Let 
^, drawn from /, perpendicular to s c, be the lever arm of 
the resistance. Let the same symbols ** primed " represent a 
new position of the system caused by the horse bending his 
knees in pulling. For simplicity, we will suppose that his 
fore feet are otf the ground and that his hind legs are not 
extended so as to increase /, as these suppositions tend to 
neutralize each other. Also that the center of gravity is on 
the line f s. 

The construction of the figure shows that, as the point s 
moves to s', c will move to c\ and that R will increase until 



XXIV. — HORSE AND HARNESS. 



the compression along s f causes the horse to bend so that / 
will shorten. 

The stress R may under these circumstances be deduced as 
follows : 

From the equaHty of moments we have W I cos i-=.r h, 

and from the figure 

. W I cos i cos ii — (p) 
i? = r cos (? — g)) = ^^ ^ 

Graphical construction shows that, as i diminishes, h and 
qp will diminish slowly, and / — qp will rapidly approach zero. 

R will have its maximum value when s falls on the line c p^ 
either from raising the point of attachment to the load at c or 
from the descent of the point of appHcation of the power at s. 
This value is not realized in practice, since, in addition to the 
effect noted above, as i decreases the force of friction at / 
decreases and the feet tend to slip. 

A proper inclination of the trace is therefore valuable since 
it enables R to be increased according to the ability and 
willingness of the horse, and also that it enables him to draw 
by increasing the friction between his feet and the ground. 

By experiment it was found that when the horse is free, 
the maximum practical value of R^ or about 0.6 W^ was 
attained for a value of i — 9 = 12°. When the horse had 
a rider, i — 9 could profitably be reduced to 7°. From 
these data it is estimated that, since tan 12°= 0.2, a draught 
horse should carry \ of his load on his back. 

The preceding general considerations apply to the case of 
men pulling on ropes or pushing on capstan bars, etc. They 
partly explain also that, while for the horse the maximum 
value of i?=0.6 W^ for man, it is found practic ''" that 
R^W, 

Arrangement of the Horses. 

Owing to the difficulty of coordinating the movement of 
the horses the single file is used only when the gait is slow 



XXIV. — HORSE AND HARNESS. 



and the road smooth, so that the shaft horse will not be un- 
duly fatigued by frequent changes of direction. 

When the double file is used, the control of the direction 
is shared by the horses of the wheel team, provided the car- 
riage have a pole. 

This team is preferably attached to a movable double tree^ 
Chapter XXI F, page 28, since this shows by its inclination 
whether the horses are pulling evenly, and also transfers the 
draught to the axis of the carriage. For these reasons it is 
often called the evener. 

By attaching the traces to the single trees hooked on to 
each end of the double tree, greater flexibiHty is attained; 
and, since the shoulders of the horse are naturally brought 
into bearing alternately, he is less apt to be chafed by the 
sliding of the collar. 

He may also, when harnessed, be more readily hitched 
and unhitched. 

In commerce the leading team is generally attached to 
an evener fastened to the front end of the pole. This is 
objectionable since it confuses the functions of the pole. 
A better method, sometimes followed, is to support the 
evener by the pole, and to connect it with the axle by an 
independent tensile member, as by a chain. 

In the present arrangement, the objections to supporting 
the weight of the evener on the end of the pole, and here- 
fore on the necks of the wheel team, are avoided, and the 
traces of each team are connected with those in rear by an 
arrangement which permits continuous draught without caus- 
ing the effort of wiUing horses to be neutralized by the 
laggards. 

The team between the leaders and the wheelers is called 
the swing team. The horse on the left of each team is 
called the near horse and that on the right the off horse. 



XXIV. — HORSE AND HARNESS. 



Requirements, 

The preceding considerations illustrate the application of 
the principle of independence of function to meet the require- 
ments of artillery harness which, as stated by another writer, 
may be thus abridged. 

" No horse should be restrained by the efforts of another, 
and the direction of the traces should be most favorable for 
draught. The drivers should be able to harness and unhar- 
ness promptly, by night as well as by day, when benumbed 
by cold and when excited by danger. The fall or loss of a 
horse should not be a permanent obstacle to the advance, 
and disabled horses should be easily replaced. ' 

U. S. Artillery Harness. Figure 2. 

WHEEL HARNESS. 

This is composed of four essential systems, three of which 
occur in all harnesses except for horses in the lead. The 
systems are : 

1st. The head gear to guide and hold the horse. 

2nd. The saddle to transport the driver, who, for the 
independent control of his team, is mounted. 

3rd. The draicght harness which enables the horse to move 
the carriage forward. 

4th. The breeching for moving it backward. 

1. The head gear consists of the bridle and halter. To 
the bit of the off horse is attached the lead rein, one end of 
which is held by the driver. 

2. All horses are saddled, the off horse carrying the driver's 
valise, and, when necessary, an extra cannoneer. 

3. The draught harness and the breeching constitute two 
independent systems symmetrically arranged. 

The former is composed of the following parts. 
The hameSj h, figure 2, are two curved irons shaped like 
the signs ( ). They are connected together below by an 



XXIV. — HORSE AND HARNESS. 



iron clasp, and adjusted at the top by a leather strap so as to 
embrace the neck and form a rigid frame against which the 
horse may thrust. To diminish the pressure per unit of area 
on the horse's shoulder* the hames rest on a similarly 
shaped cushion, the collar. To each hame is attached by a 
flexible hinge a stout leather tug^ t. This terminates in an 
iron ring through which passes the trace chain, c^ terminated 
by the toggle^ t' . The latter connects the front trace chain 
of the wheel horse with the rear trace chain of his leader, 
and so on throughout the column. When in motion, the tug 
ring plays on the trace chain and thus makes the leading 
horses independent of those in rear. 

The length of the rear trace chain may be varied by a 
toggle to suit the conformation of the horse. 

The safe, s, protects the shoulder from chafing. 

The loin strap, /, sustains the trace when relaxed, and the 
belly band beneath the saddle keeps it from rising over the 
back in turning. 

4. The breeching is composed of the broad breech strap, 
b, figure 3, corresponding to the collar ; it is supported by 
the hip straps h. Corresponding to the traces is a Y-shaped 
system consisting : — 1st. Of the continuous breast strap, bs, 
which, passing around the breast, is united at each end to the 
breech strap. It is supported in front by iron Hnks hanging 
from the hames. 2nd. The stem of the Y is formed by the 
pole strap, p, connected at one end to the breast strap by an 
iron double-loop, shaped like a figure 8, and leading obliquely 
downward and inward to the end of the pole. The functions 
of the pole thus correspond to those of the splinter bar 
in rear. 



* This end is served in modern practice by using hames of sheet steel 
formed to fit the shoulder. The same principle is applied in the cavalry 
saddle. 



XXIV. — HORSE AND HARNESS. 



Pole Yoke, 

The weight of the pole is supported by the pole yoke, 
which is connected by a short chain to the clasp of the 
hames. The branches of the yoke are so hinged to a collar 
revolving loosely around the pole that they can play only in 
a plane passing through the axis of the pole. 

This allows the horses to travel freely at different levels 
and prevents the lateral thrashifig of the pole. 

LEAD HARNESS. 

The leading horses have longer traces than the wheelers 
and have no breeching; otherwise their harness is identical. 

Improved Harness. Figure 4. 

The harness devised by Major Williston of the Artillery, 
which is now undergoing trial, resembles that above described 
except in the following principal points. 

1st. For interchangeability, the saddles and bridles are 
the same as those used by the cavalry, and saddle bags 
replace the valise. 

2nd. The wheel traces are attached to single trees which 
may be hooked to the saddle when not in use. 

3rd. The breeching is that used in commerce. The stem 
of the Y passes under the horse to a transverse bar in front, 
which corresponds to the evener, and is called the neck yoke. 

This is the most important change from the regulation 
harness. It prevents the breech strap from slipping upward 
in stopping suddenly, and also avoids the oblique thrust on 
the horse's neck which tends to make him fall. 

The neck yoke also controls the pole better than the hinged 
pole yoke. 

4th. The bridle rein of the off horse passes through a 
pulley on his saddle, so that, in holding him back, the 
oblique stress above mentioned is further avoided. 



XXIV. — HORSE AND HARNESS. 



5th. The collar, instead of being continuous, is hinged 
above and is provided with a fastening below in easy reach. 

6th. The horse of the chief of piece is provided with a 
light draught harness, consisting of a breast collar and traces, 
with which in an emergency the other horses may be assisted. 
When not in use the traces are folded across the horse's 
withers. 

This harness is distinguished for the ease with which the 
horses may be detached from the carriage in all conditions of 
service. 

LEATHER. 

That used in harness is classified according to its thickness, 
into harness," bridle and collar leather. 

The leather from the necks, shanks, flanks and bellies, or 
the offal, figure 5, is rejected as too spongy for use, so that 
only about one-half of the hide is employed. Of this, the 
butt is the best portion. 

The lighter hides are slit axially into sides. 



XXV. — ARTILLERY MACHINES. 



CHAPTER XXV. 

ARTILLERY MACHINES. 
Object- 

Artillery machines are employed to mount and dismount 
cannon and to transport artillery material from one part of a 
work to another. They comprise the gin, the gun lift and 
Jacks of various forms; and wheeled vehicles such as the sling 
cart, the truck, etc. 

Machines Used in Mounting Cannon. 

The gin consists of a tripod composed of two legs which 
form a shear or derrick, and a pry pole by which the legs 
are lifted and braced. 

The hoisting apparatus consists of a block and fall sus- 
pended from the apex and operated by a windlass supported 
by the legs in a position convenient for the use of handspikes. 

The use of the gin is confined to relatively light weights. 
Heavy weights are preferably lifted by the hydraulic jack and 
loose blocking. 

The hydraulic jack is a compact form of the hydraulic 
press, which contains within itself the reservoir of liquid 
required. It is provided with valves by which the direction 
of the motion of the ram may be varied. 

Other jacks apply the principles of the lever and the screw, 
and are correspondingly named. 

The gun lift consists of two massive trestles so framed that 
they may be easily dismounted for transportation. 

Each trestle carries on its beam a hydraulic jack ; the latter 
by means of a lever raises a bar of iron which passes verti- 
cally through the beam and the lever, between the jack and 
the fulcrum of the lever. This bar is pierced at short inter- 
vals by holes, and its lower end is formed into a hook. 



XXV. — ARTILLERY MACHINES. 



Both bars having been attached to the weight, and a pin 
having been passed through the hole in the bar next above 
the lever, the ram of the jack is raised to its full extent. A 
pin is then inserted through the hole next above the beam 
and the ram is lowered. The upper pin is then shifted down- 
ward and the operation continued. 

For comparatively light weights a single trestle may be 
employed like a gin. 

Machines Used in Transportation. 

Heavy weights are usually transported by the aid of cap- 
stans and rollers. 

When space permits, cannon may be rolled bodily by par- 
buckling. In such cases a muzzle collar of the maximum 
diameter of the piece corrects the circular path which the 
conical mass tends to describe. 

Heavy weights may also be rolled through the narrow 
passages of forts on a low framework called the cradle. 

The wheels of sling carts are large and have but little dish. 
Since, hke the gin, they suspend the load, they are relatively 
weak, and hence are used for lighter weights than the cradle. 

By mechanical appliances mounted on the axle, the weight 
may be lifted from the ground, and during transportation 
may be permanently secured to the axle by hooks which 
relieve the more delicate mechanism from shocks. 

The means of lifting are the screw, and the hydraulic jack 
which works on the principle explained for the gun lift. 

For light weights the eccentric position of the hooks may 
enable the weight to be raised by lifting the pole before the 
weight is attached and afterwards by depressing it. This 
means of lifting is applied to the iron sling cart. The field 
limber may be similarly used to carry a piece, the carriage of 
which is disabled. 

In transportation the pole of the sling cart is supported by 
the limber. 



XXVI. — HAND ARMS. 



CHAPTER XXVI. 

HAND ARMS. 

The weapons carried by the soldier, or portable arms may 
be divided into hand arms and small arms. 

The former class is known in French as '^armes blanches ; " 
the latter requires, as in cannon, a preliminary study of the 
ammunition employed. See Chapter XXVII. 

Classification. 

Hand arms are divided into 

1st. Thrusting arms which act by the point. 

2nd. Cutting arms which act by the edge. 

These functions may be combined in the same weapon, 
though at some sacrifice of efficiency. 

Thrusting Arms. 

The body of a thrusting weapon should be straight so as 
to avoid a rotary moment on impact, and the center of gravity 
should be placed near the handle. This may be attained by 
fluting the blade, or by suitably weighting the handle. 

The principal thru^sting weapons are the straight sword, the 
lance and the bayonet. 

The sword is composed of the blade, the hilt by which it 
is held, and the guard. A knob sometimes acts to counter- 
poise the blade as in the foil. 

The lance is composed of a short steel blade fixed to the 
end of a wooden handle about 10 to 16 feet in length. The 
handle is furnished with a leather arm-loop placed over the 
center of gravity. 



XXVI. — HAND ARMS. 



After a long period of comparative disuse, in spite of the 
greatly increased efficiency of small arms, its use abroad is 
now becoming more general. In this country it has never 
been successfully employed. 

The bayonet is useful principally for guard duty and for 
its moral effect. Like other hand arms, it has the merit of 
"never missing fire." 

The objections attending its weight and that of its scab- 
bard, and its eccentric position in firing may be partly over- 
come by combining its functions with those of the ramrod. 
Attempts have also been made to turn it into an intrenching 
trowel. The tendency is now to shorten it to the proportions 
of a dirk, which may form a useful knife. 

Cutting Arms. 

The efficiency of these arms is promoted by increasing the 
distance of the center of gravity from the handle, and by giv- 
ing a curvature to the cutting edge so as to develop on impact 
a tangential or slicing component which will call into play 
the serrated edge possessed by even the sharpest knife. This 
enables the weapon to rupture in detail the muscular fibers 
on which it acts. 

Description. 

The principal cutting weapon is the saber. Sabers are 
classified according to their use. In the U. S. service there 
are two kinds, viz. : the cavalry saber and that for the light 
artillery. 

The cavalry saber, being used on horseback for thrusting as 
well as for cutting, has but a slight curvature, a long blade, 
and a basket hilt (properly a guard) which carries the center 
of gravity toward the handle. 

The light artillery saber being intended for hand to hand 
conflict by troops, who for the service of their batteries are 



XXVI. — HAND ARMS. 



dismounted, is shorter than the cavalry saber, is more curved, 
and has a guard composed of a single scroll of brass. 

Remarks. 

The present tendency is to make the artilleryman depend 
for his personal defence upon the gun which his duty to the 
other troops compels him to serve to the very last extremity. 
He should therefore be free from any incumbrance which 
will distract him from his proper functions. 

In order to avoid the exposure of the person in cutting, 
many cavalry officers are in favor of avoiding the objections 
to the combined functions of the cavalry saber by using it 
solely for thrusting. 

On the other hand the swordsmen of East India, than 
whom there are few more expert, prefer blades which are 
greariy curved, the radius of curvature of some being about 
18 inches. 

The following discussion illustrates the effect of curvature, 
frequently utilized in the useful arts. 



^ "-V s' ^'"' 

Let O S Ph^ the edge of a curved blade rotated around 
O and striking at P with a blow, P F, at right angles to 
OP, ThenP T=PPcQS(p =PF cos i^ Z' r is the tan- 
gential component, and this will be measured by P P cos 
C P Oj which gives an easy method of discussing the effect 
of curvature. If, as in the artillery saber, S', the radius of 



XXVI. — HAND ARMS. 



curvature, be shortened by placing the center at C ; or, if 
as in some Eastern blades which have a tangential handle and 
also in the common scythe, the center of rotation be placed 
above the line P O, the value of cos (p will be increased and 
so will the proportionate value of the tangential component. 
On the other hand if, as in the cavalry saber, the handle 
be lowered as to O, in order to increase the tangential com- 
ponent in thrusting, the slicing component will decrease. 



XXVII. — SMALL ARM AMMUNITION. 



CHAPTER XXVII. 

SMALL ARM AMMUNITION. 

The Eelation between Arms and Ammunition. 

As seen in Chapter V, the efficiency of all fire arms has 
been dependent principally upon the nature of their ammu- 
nition. 

This may be called the food of the gun as the means of 
conveying it to the chamber is actually called the feed. As 
a rule the gun must be made to fit the ammunition as a shoe 
should be made to fit the foot. 

MUZZLE LOADING AMMUNITION. 

Powder and ball were originally carried loose; but for 
some time the greater rapidity of fire with arrows at the 
ranges common to both weapons, caused the latter to be 
preferred. 

Gustavus Adolphus made important improvements in the 
ammunition. 

He first provided separate receptacles for each powder 
charge ; these were called cartridges from their paper 
envelopes. (Latin charfa, paper.) 

He subsequently combined the powder with the projectile 
in the paper wrapper, which, until about 1865, formed the 
principal ammunition for small arms. See Figure 1. 

In addition to the comparative disadvantages of muzzle 
loading arms cited in Chapter XI, may be named the vari- 
able amount and condition of the powder in the chamber, 
since the powder was but imperfectly protected from moist- 
ure and was hable to be wasted in loadmg. There was also 



XXVII. — SMALL ARM AMMUNITION. 



the danger of inadvertently loading tlie piece with more 
than one cartridge at a time. Nearly one-half of the 
muskets abandoned at the battle of Gettysburg were found 
to contain more than one cartridge. 

In spite of the theories of those who feared that increased 
rapidity of fire would lead to a disastrous expenditure of 
ammunition, there has always been the feeling expressed by 
Frederick the Great in saying, that other things being equal, 
" He who fires fastest hits most." 

BREECH LOADING AMMUNITION. 

Non-metallic Ammunition. 

The state of the arts required the first breech loading 
ammunition to be formed after the manner of that just 
described ; and, as it was impossible to permanently prevent 
the escape of gas by the close fitting of the parts of the 
breech, the joint required for rapid loading was generally 
placed in front of the chamber, from which position the 
soldier would suffer least from the discharge. 

To facilitate loading the section of the barrel containing 
the chamber was caused to oscillate about an axis in rear; 
so that, the paper cartridge having been broken for loading, 
the bullet acted as a stopper to prevent the exposure of the 
loose powder before the piece was closed. 

This structure distinguishes a large class of arms, now 
obsolete, which are known as having 7novable chambers. 
This includes the Hall rifle, used in this country in the early 
part of the century. It is believed to be the first breech 
loading small arm used by troops. 

The operation of such guns was necessarily slow and 
defective. 

METALLIC AMMUNITION. 

Origin. 

The primed metallic cartridge case, invented in France, 
was first used by troops during our Civil War. It contained 



XXVlt. — SMALL ARM AMMUNITION. 



all the components of the ammunition, under invariable con- 
ditions, in an envelope which formed a gas check, and was 
therefore adapted to arms in which the chamber was fixed. 

Being rigid and of exact dimensions it could be and was 
at first most extensively used in magazine arms, in which 
the operations of loading are automatically performed. 

Rim Fire. 

In order to support it against the blow which exploded the 
fulminating priming, and to extract the empty case, it was 
provided with a rim. For simplicity of manufacture, and 
because the arms in which it was principally employed con- 
tained the cartridges in tubular magazines and were carried 
by mounted troops, the fulminate,/, was placed within the rim, 
as shown in figure 2. 

This construction, although confusing the functions of the 
rim and the primer, was intended to prevent accidental ex- 
plosions in the magazine. 

For the small charges of powder then used, the metal could 
be made thin enough for certainty of fire, since it was com- 
posed of soft copper. 

Figure 2 shows that such a cartridge, having what is termed 
a folded head, is necessarily unsupported by the walls of the 
chamber for a length at least equal to the thickness of the 
metal forming the rim. Consequently, as charges and pres- 
sures were increased, the rim fire cartridges were found to 
shear across the edge of the chamber ; and the copper was so 
deficient in elasticity that they would resist extraction. 

The quantity of fulminate contained in the rim was much 
greater than was required for ignition at any one point, and 
further tended to destroy the fold. The distribution was im- 
perfect and misfires were frequent. 

The cartridge could not be reloaded. 



XXVII. — SMALL ARM AMMUNITION. 



Central Fire. 

As metallic ammunition became more generally employed 
in all arms, these objections led to the use of the center fire 
cartridge, now universally employed ; these objections led 
also for a time to the disuse of magazine arms. 

The adoption of central fire permits the case to be strength- 
ened indefinitely in the shearing plane ^ and to be made of 
an elastic material like brass, the special elasticity of which, 
developed by its manufacture, facilitates its extraction. It 
also permits the reloading required by the great expenditure 
of ammunition m target practice. 

Folded Head. 

The first center fire cartridges were made with folded heads, 
as the arts then furnished no other method of forming the rim. 
To avoid shearing, a thin, cup-shaped, gas check, as shown in 
figure 3, was, and is still employed. This contains a central 
hole to allow the flame from the fulminate, /, to pass through 
the vents, vv^ in the anvil, a. 

The Ordnance Department for several years made the copper 
cup-anvil cartridge shown in figure 4. In this it was attempt- 
ed to combine in one piece the functions of the gas check 
and of the anvil. But these were inconsistent, and the cart- 
ridge, although avoiding objections urged against a per- 
forated head which contained a loose primer, was abandoned. 

The limit of resistance to shearing was soon reached, 
because, owing to the manufacture, the maximum thickness of 
metal is that of the head. So that if a thicker or more elastic 
metal was used misfires would result, unless the energy of the 
blow required for ignition was so much increased that the 
rapidity of fire was diminished. 

The flat anvil, figure 5, demanded by the obhque firing 
pin of the Springfield rifle, requires a more powerful blov/ 
than does that shown in figure 3, and the thickness of metal 



XXVII. SMALL ARM AMMUNITION. 



requires the firing pin to be sharp. On the other hand, the 
anvil of figure 3 is well adapted to the axial blow of a flat 
pointed pin. This requires less work in cocking and is less 
apt to pierce the cap. 

Solid Heads. 

The state of the arts now permits the U. S. cartridge to be 
made with a solid head, as in figure 5. The shearing plane 
lies in front of the edge of the chamber even when, owing to 
the yielding of its support, the case may be forced backward 
in firing. 

Certainty of ignition now requires that the anvil shall be 
renewed at every fire. Consequently the primer is assembled 
before issue with its anvil and fulminate complete. The 
resulting variation in figure 3 is shown in figure 6. 

An objection to the solid head cartridge arises from its un- 
equal expansion when fired. The mouth, being thin, is more 
firmly held by friction against the walls of the chamber than 
is the thicker portion in rear, so that the latter may slide 
backward to the extent permitted by its support. Cases 
which have been often reloaded are found to tear across by 
longitudinal stress. 

The Morse cartridge, figure 7, provides for this by making 
the head entirely separate from the body of the case. 

Remark, 
The influence of improvements in metallic ammunition has 
probably reached its limit in the cartridge employed in rapid 
firing cannon, Chapter XXIX, page 18. The size of the 
cartridges which these employ is limited by the weight which 
one man can conveniently handle. 

METALS USED FOR CARTRIDGE CASES. 

Copper was first employed on account of the ease with 
which it could be worked. When alloyed with a small pro- 



XXVn. — SMALL ARM AMMUNITION. 



portion of zinc it was until recently preferred by the U. S. to 
brass, which, when in contact with gun powder, undergoes in 
time a molecular change that renders it as brittle as baked 
clay. It is said that the discovery of this defect in the 
Russian ammunition postponed the war of 1877. 

The deficient elasticity of copper accounts for the preva- 
lence of the lever used for extraction in early breech loading 
arms, and for their comparative slowness of fire. 

Brass is cheap and so elastic that guns in which it is used 
may be opened by the direct action of an axial bolt. For 
the reasons given, Chapter XXVIII, page 6, the rapidity of 
fire of such arms is increased. This is the metal now 
generally employed. In order to protect it from the powder 
the cavity may be varnished or tinned. 

The elasticity of brass adapts it to reloading since resizing 
is less necessary than with copper. 

The operation of resizing is required by unavoidable dif- 
ferences in the chambers of different guns. The brass cart- 
ridges used in the rifle, Cal. 0.45 may often be reloaded for 
use in the same gun without resizing them ; but owing to the 
greater pressures found in the new Cal. 0.30 rifle, firing smoke- 
less powder, resizing is always required for this arm. See 
Chapter XXVIII, page 3. 

Low steely when protected from oxidation, is proposed as a 
cartridge metal, on account of its strength elasticity and 
freedom from structural change. 



MANUFACTURE OF METALLIC AMMUNITION. 

The cartridge case may be made in two general ways, 
viz. : 1st, by coiling by hand a thin sheet of metal into a 
tube ; 2nd, by drawing the tube from a thicker disc as de- 
scribed in Chapter XVIII, page 2. 



XXVII.— SMALL ARM AMMUNITION. 



1. Wrapped Metallic Cartridges. Chap. XVI, figure 8 

The metallic sheet is trapezoidal so as to increase the 
thickness of the walls near the head. This gives the ex- 
terior the conical form required for extraction, while the 
interior being cylindrical retains its hold on the bullet. It 
also increases the thickness of the flange by which the 
case is riveted to Ihe separate disc that forms the head. 

This method, the origin of which is evident, avoids the 
use of the expensive machinery used in the second process, 
so that in an emergency the manufacture could be easily 
improvised. 

The cartridge is serviceable, but neither waterproof, rigid, 
nor exact enough in its dimensions, for all the requirements 
of service. 

2. Drawn Cartridges. 

The operation of drawing necessarily leaves the exterior 
of the tube cylindrical, so that the required variation in 
thickness is obtained by varying the diameter of the 
punch. 

The primary draws are facilitated by removing by an- 
nealing, (/. ^., heating followed by quenching), the special 
elasticity developed by the previous operations. Chapter 
XV, page 22. 

After having been drawn to a length slightly in excess of 
that required, the tubes are trimmed to an exact length to 
prepare them for the operations of heading. 

The mandrel, figure 8, supports the trimmed case in a 
closely fitting die. A hunter of the proper dimensions first 
forms the pocket for the primer, and a second operation with 
a bunter, such as shown, causes the metal to flow into the 
annular space provided for the rim. The pocket is then 
vented. 



XXVII. — SMALL ARM AMMUNITION. 



To facilitate extraction the case is tapered by forcing over 
it a conical die. The cylindrical seat for the bullet is 
simultaneously formed. 

Components 

The U, S. atwil is made from a copper wire of rectangular 
cross section containing on one side a continuous groove. 
From this are punched a series ot circular discs which form 
the anvils, The edges of the discs are notched so as to 
form a passage way for the flame of the fulminate,/, through 
the notches, into the groove which bridges over the vent, z/, in 
the head of the cartridge. 

The bullet is composed of an alloy ot lead and tin ; the 
latter metal, although it increases the difhculty of manufac- 
ture, gives the hardness required to resist deformation in 
the gun. Chapter XXVIII, page 3. 

The bullet is made by compression between dies which 
part on an axial plane. See figure 9. The cavity in the 
base of the bullet may be varied to bring the bullets to an 
exact weight. 

The bullet is lubricated by being forced through a vege- 
table wax so as to fill the cannelures, or grooves. This is 
preferred to a fat, as it does not corrode the metals in store. 

Common Operations 

In the loading machine a measured charge of powder is 
first deposited in the case and slightly compressed so as to 
increase the density of loading. The bullet is next inserted 
and secured by crimping the case upon it. 

The finished cartridges are all inspected for weight and 
dimensions. 

The first is accomplished by a weighing machine which 
rejects all that weigh less than a prescribed minimum. The 
principal object of this operation is to detect charges in- 



XXVII. — SMALL ARM AMMUNITION. 

sufficient to expel a projectile which might cause a subse- 
quent discharge to burst the gun. 

The gauging machine makes sure that every cartridge 
will enter the gun. The gauging die, which is sUghtly 
smaller than the minimum chamber, verifies the length of 
the cartridge to the rear from the circle of contact between 
the bullet and the rifling, the profile between these planes, 
and the maximun radius of the rim. 

For safety the primer is sunken below the plane of the 
head. 

The automatic operation of the machinery has greatly 
reduced the cost of manufacture, and has thus removed one 
of the principal objections to metallic ammunition. 

The inspection merely precedes the proof. Chapter 
XVII, page 18. This consists in firing a portion of the 
daily product to verify the certainty of fire, the strength of 
the case, to determine the volume of the charge, the com- 
pression required for the standard velocity and above all to 
test the accuracy of fire. 

U. S. SMALL ARM AMMUNITION. 

The following varieties are now made (1891) : 

1. The rifle ball cartridge, /^^q, or about 70 grains of 
powder and a 500 grain bullet. / V= 1280 / s. 

2. The carbine ball cartridge, /o\- ^ ^-= 1150 / s, 

3. The revolver ball cartridge, f^^. I V= 730 /j-. 

4. The rifle and carbine blank cartridge, filled with com- 
pressed powder that is protected by a varnished paper cup, 
and retained by crimping the case so as to facilitate loading. 

5. The revolver blank cartridge as in 4. 

Important changes in this ammunition are now pending. 
Their principles will be hereafter discussed in connection 
with the arm. It is significant to observe that now, as here- 
tofore, the adoption of the new arm awaits the perfection of 
its ammunition. Chapter XXVIII, page 19. 



XXVIII. — SMALL ARMS. 



CHAPTER XXVIII. 

SMALL ARMS. 
Classification. 

Small arms may be classified according to the service in 
which they are employed, as this determines the maximum 
length of barrel, given to the rifle^ i\\Q carbine^ and W^q pistol. 

Muzzle-loading arms, and breech-loaders having movable 
chambers being now obsolete, breech-loading small arms 
with fixed chambers may be classified into single loading and 
magazine arms. 

The latter class is now supplanting the former, because of 
the moral and physical advantage of being able at will to 
increase the rapidity of musketry fire. 

Historical Sketch. 

Some of the objections formerly made against the breech- 
loader have been discussed in Chapter XXVII. To these may 
be added the former fear that the mechanism might not endure 
the accidents of service. 

But the Prussian wars of 1864 and 1866, and the more 
extended campaigns of 1870, proved that after a victory 
there is generally time enough for repairs. 

During the siege of Plevna in 1877, these conclusions 
were emphasized by the use by the Turks, for the first time 
in Europe, of the American Winchester repeater. 

Although of a model now considered imperfect, its success 
was conclusive. 

It is now realized that the change from muzzle-loading to 
breech-loading having established the advantages of rapidity, 
the choice of a magazine arm is a detail to be determined by 



XXVIII. — SMALL ARMS. 



independent considerations. The selection is attended with 
many complications which, as in the past, relate principally 
to the ammunition. Some of these will be hereafter dis- 
cussed in detail » but it may be premised that, while the 
power ol the weapon depends principally upon the abiUty of 
its (human) carriage to resist recoil ; its continued operation 
depends upon the number of cartridges which this carriage 
can conveniently transport. 

The development is thus limited by a physical constant. 

COMPONENT PARTS OF B. L. SMALL ARMS. 

I. THE BARREL. 

Weight. 

Except for considerations relating to the recoil and the 
practical necessities of service, the general use of steel would 
permit the barrel to be considerably reduced in weight. 

Caliber. 

Although the best results follow from adapting to each arm 
its own ammunition, yet in order to meet emergencies the 
cartridges for the rifle and the carbine may be interchanged. 
These arms are therefore of the same caliber. 

For the reasons stated in Chapter XVI, since the adoption 
of the rifle principle the tendency has been to reduce the 
caliber. The limit is fixed by questions of internal ballistics, 
and also by the nervous shock communicated to the animal 
struck. Upon the shock is thought to depend the " stopping 
power " of a bullet that does not kill. 

Until lately the limit was generally taken at about 0.45 
inch, but recent experiments have induced many countries to 
reduce it still further to about 0.30 inch. 

The propriety of the change is still debated, and like many 
others requires the test of war. The advantage may consist 
in this : that a shock which might be insufficient to stop a 



XXVIII. — SMALL ARMS. 



man in the heat of a close action may, at the long ranges 
which the reduced caliber provides, be severe enough to cause 
him to withdraw. But this would not apply to horses. 

Rifling. 

The cross-section of the rifling depends principally on the 
nature of the bullet. If this be of a soft material, like lead, 
the lands may be broad as in the Springfield rifle and con 
versely, figure 15, if the metal be hard. The grooves should 
be shallow and so formed as to be readily cleaned. 

The increase of spherical density, which results from 
reducing the diameter of a projectile of which the length, 
and therefore the sectional density, is kept nearly constant, 
has required a considerable increase in the twist, so that 
special precautions have been required to prevent the pro- 
jectile from shearing. Chapter XVI, page 10. 

In the caliber 0.45 bullet this was done by alloying the lead 
with tin, Chapter XXVII, page 8 ; the new bullet is more- 
over coated with a thin jacket of a harder metal. Chapter 
XXVII; Plates. 

II. THE STOCK. 

This forms the handle by which the barrel is directed. It 
is made of wood on account of its lightness and strength and 
its deficient conductivity of heat. 

The form of the stock depends on the conformation of the 
average man. 

The butt is widened and curved so as to diminish the 
pressure per unit of area due to the recoil. It is bent for 
convenience in aiming. A rotary component of recoil is 
thereby developed, which, if the crook be excessive, may 
cause inconvenience to the firer. 

The stock is necessarily weakened by being cut across the 
grain to form a grasp, and more so by the present develop. 



XXVIII. — SMALL ARMS. 



ment in the volume of the parts about the breech It is 
consequently frequently made in two pieces, the /// stock 
being of a rigid material, such as black walnut, and the butt 
itoik preferably tough, as of elm. Chapter XV, page 12. 

The support m rear of the barrel should be of sufficient 
area to avoid permanent deformation; and that beneath the 
barrel should not be unduly rigid, since otherwise the barrel 
may be distorted by the effects of moisture upon the wood. 



Ill THE SIGHTS. 

The position of the rear sight is determined by the limit of 
distinct vision, and is so taken that the two sights and the 
object shall collectively be most plainly seen. 

The sights are separated as far as convenience permits, so 
as to rectify their ahgnment with the object. See Chapter 
XXX, page 7. They admit of a permanent correction for 
jump and a variable correction for range, drift and the effects 
of wind. 

The increasing flatness of the trajectory and the growing 
rapidity of fire will, except for sharpshooters, probably 
diminish the number of adjustments now given to the rear 
sight. 

It is probable also, that instead of providing an extension 
to the slide for use at extreme ranges, a separate pair of sights 
will be placed on the side of the arm. The ordinary func- 
tions of the members of this pair will be reversed; that is, the 
rear sight will be fixed and the front sight movable down- 
ward, so that a considerable elevation may be attained with- 
out great variation in the relative positions of the eye of the 
marksman and the point of his body which receives the recoil. 

It may be remarked that the requirements of sights for war 
service and for target practice at kiiowti distafices are in many 
essentials incompatible. 



XXVIII. — SMALL ARMS. 



[V. THE MOUNTINGS. 



The bands, screws, pins, etc., are intended to connect the 
parts ; and the butt plate, tip and the extension of the guard 
beneath the small of the stock are intended to protect from 
wear and to strengthen the relatively perishable wood. 



Functions. 



V. THE BREECH MECHANISM. 



The functions of the breech mechanism are five, viz. : to 
open, load and lock the breech, to fire the charge, and to 
remove the empty shell. 

The manner in which these functions are performed 
depends primarily upon the manner of opening and closing 
the breech, as is shown by the following scheme : 

Classification of B. L. Small Arms.* 



o 2 

a> ? 

u ^ 



■5 « 

as 



Barrel, 
which 



slides 



b 



...2. 
...3. 



Breech 

block 

which 



rotates 

about J JUo axis of gnn. 
an axis 1 Lto axis of gun. 
which is [ 

slides I Jltoaxis of gun 4. 

^^'"^^ 1 Lto axis of gun 5. 



f 1 1 to axis of gun 6. 

fin front of block 7. 




L to axis . 
of gun. 1 



not in front of 1 
block. I 



No. Examples. 
(Rare). 



Revolvers t 
Shot guns. 



Bolt guns. 
Sharps, (Krupp). 

Joslyn, Warner. 
( Springfield, 
I Remington. 

Martini. 



, movable chambers (obsolete) 9. Hall, Burnside. 



Discussion of Table. 

The mass of the barrel renders the classes, 1, 2, 3, unsuit- 
able for the military service except when, as in revolvers, the 
mass is greatly reduced. 



* For a fuller discussion, see Report Chief of Ordnance, 1873. 

t The classification ot these is difficult. For some reasons they may 
be considered as movable chambers, and in other respects they may be 
considered as an aggregation of barrels of reduced length. 



XXVIII. — SMALL ARMS. 



Classes 5, 6, 8, are objectionable, as their operation does 
not assist in loading the cartridge, but rather, as the French 
say, to guillotine it. 

They possess, however, the advantage of naturally resisting 
the pressure which tends to blow open the breech or to 
" unlock'' it. 

Class 7 naturally forms a lever, formerly useful in forcing 
into the chamber a deformed cartridge or in extracting one 
that stuck. Arms of classes 4, 5 and 8 were frequently pro- 
vided with levers. 

Bolt System. 

But, as the quality of the ammunition has improved, the 
arms of class 4 7vithout levers^ have grown mto general use. 

The following are the principal objections which have 
hitherto prevented the more general adoption of the bolt gun, 
although its advantages were recognized by the Prussians as 
early as 1847. 

1. The risk of premature discharge from striking an over- 
sensitive cartridge in loading. 

This was long considered an insuperable objection, but, as 
will be seen, has been overcome by very simple means. 

2. The danger resulting from the necessity of loading the 
piece at a full cock. 

This objection neglected the supreme advantage of the 
rapidity of fire which results from suppressing a discontinuous 
motion,* and which is further increased by the facihty with 
which the reciprocating motion of the bolt adapts itself to 
the demands of magazine arms. 

To illustrate the latest type of this arm, the American 
Lee system is described, as it contains in probably the best 



*The word is used as in the drill book. 



XXVIII. — SMALL ARMS. 



and simplest form the elements of the mechanism required 
for performing the functions above named.* 

Lee System (as single loader) Figures 1 and 2. 

Descripiion, 

The receiver, of approximately cylindrical form, is screwed 
to the breech and receives the mechanism. It is bored out 
and slotted to permit the axial motion of the bolt. The slot is 
widened to the front to form the well of the receiver, through 
which the operations of loading and ejection are performed. 

The rectangular shoulder at a forms a support for the locking 
mass, a\ of the bolt in firing, and the oblique edge at b gives a 
short, spiral motion to the bolt as the locking mass is ap- 
proaching or leaving its support. 

The system is mortised vertically through the well to receive 
the magazine. As this is a special feature of the arm, its 
consideration is deferred until the features common to the 
best bolt guns have been discussed. 

The reciprocating motion of the bolt sets the whole 
mechanism in motion. 

The /ia7idle is placed in rear and is curved downward so 
that the hand need not leave it in firing. 

A lug diametrically opposite to the locking mass engages 
with a corresponding recess in the bore of the receiver, so 



*The Prussian Needle Gun used a combustible cartridge case, the 
fouling from which tended to obstruct the chamber ; the joint was most 
imperfectly sealed, the flames escaping not only around the end of the 
bolt, but into the channel traversed by the firing needle. The tactical ad- 
vantages of the arm, however, offset these very serious objections, so 
that it was retained unchanged until adapted to metallic ammunition 
after the war of 1870. 

Its opponent in this war, the Chassepot, was of similar construction, 
but possessed for the end of the bolt a gas check, from which that of 
Colonel De Bange is derived. 



XXVIII. — SMALL ARMS. 



that, by making the support symmetrical, certain objectionable 
vibrations of the barrel may be avoided. 

The bolt contains an axial firing pin which is surrounded 
by a spiral main spring and secured to the hammer. 

The bolt carries in front and to the right a hook shaped 
extractor^ which, like the hammer, is so disposed as to share 
only in the motion of translation which the bolt receives. 
The extractor is retained by a flat spring which serves also to 
key the system together. 

Operation. 

To open the piece, raise the handle so that the locking 
mass may lie in the prolongation of the slot, and withdraw 
the bolt. 

The incipient rotation of the bolt is ingeniously commuted 
into one of translation at each of its ends ; as follows : — 

In rear, a radial projection on the bolt strikes an oblique 
surface on the hammer and forces it back relatively to the 
bolt until the point of the firing pin is retracted, or withdrawn 
behind the plane surface in contact with the cartridge. To 
avoid premature explosion the point of the firing pin is kept 
back until the desired moment of discharge. 

In front, the spiral motion due to the surface, b, forces the 
bolt slowly back from the barrel so that power is obtained to 
start the fired cartridge case from its seat. This slow and 
therefore powerful motion of extractiofi is commonly used. 
A rapid motion might cut through the cartridge rim and dis- 
able the rifle. 

As the bolt is withdrawn, the extracted case foflows until it 
passes from the chamber. The rim then strikes the ejector 
stud, a projection on the bore of the receiver opposite to the 
path of the extractor. The case is thereby rapidly revolved 
about the hook and ejected, or thrown clear of the gun. 

A cartridge may then be dropped into the well, the bottom 



XXVltl. — SMALL ARMS. 



of which is nearly continuous with the lower element of the 
chamber. A reversal of the motions forces the cartridge into 
,<lace and locks the breech. 

The surface, ^, now serves to prevent the shock referred to 
on page 6, and also to make the motion of the hand con- 
tinuous. 

In the final motion of closing, the mainspring is fully com 
pressed, or the piece is cocked, by the interposition of the 
sear, the nose of which arrests the forward motion of the 
hammer while the bolt moves on. 

The U shaped sear spring acts against the trigger through 
the sear; so, that when the trigger is drawn, the sear spring 
is compressed, the sear is lowered -and the hammer allowed 
to fall. 

Remarks. 

Opening^ closing and loading. These operations are safely 
and rapidly performed. 

Locking, The method is of great simplicity and affords a 
sohd support. Jointed surfaces, however well made, permit 
an objectionable displacement under the stress of firing. 

Firing. The coiled spring is admirably adapted to the 
purpose, since, owing to its developed length, the stress on 
any of its spires is slight ; and, owing to its position on the 
pin, it will continue to work, even if broken. 

Extraction and ejection. These are readily performed, 
Vven with inferior ammunition. 

Assembling. The parts are few in number, strong and simple. 
They are arranged so as to avoid the effects of rust and dust, 
and are so connected as to be readily dismounted for cleaning 
without the use of special tools. 

MAGAZINE ARMS. 

If by any means a succession of cartridges can be auto- 
matically placed in front of the bolt as it is closing, a mag- 
azine gun will result. 



10 JCXVIIl.— SMALt ARM§ 



This has been accomplished in many ways which may be 
classified. 1st. According as the niagazmes are tubular, or 
box shaped, 2nd. According as they are permanently fixed 
to the gun, or are detachable. The tubular magazines are 
always fixed. 

TUBULAR MAGAZINES. 

These may lie either, 1st, in front, as beneath the barrel, 
or 2nd, in the cylindrical volume lorming the small of the 
stock and its prolongation in rear. 

A spiral spring forces the contents of the tube toward the 
receiver, and a valve regulates their entrance. 

In the first class a carrier, operated by the withdrawal of 
the bolt, raises the cartridges successively from the mouth of 
the tube to the mouth of the chamber. See figure 3 for one 
form of carrier. 

The operation is that of the bell crank. Chapter XXIX, 
figure 7^ 

Advantages. 
This form of magazine, used in the French Lebel Rifle, 
adapts itself to the profile of the gun. When in front, the 
capacity is large for cartridges which are short and thick, and 
a simple trap door on the side permits the magazine to be 
filled without opening the breech, /. e., luithout unloading the 
gun. 

Disadvafitages. 

The cartridges lie end to end, and in firing are exposed to 
shocks which may explode them or deform them sufficiently 
to interfere with the regularity of the feed. 

The feed acts in the direction of the longest dimension of 
the cartridge. 

For the front magazine the weight is not well distributed ; 
and for that in the butt the capacity is smal^, and the filling 



XXVIII. — SMALL ARMS. 11 

of the magazine is complicated with the unloading of the 
gun. 

The operation of filling is slow, since the cartridges are 
passed in singly ; and, since nothing external indicates the 
state of the supply, the control of the fire by the soldier, and 
of the soldier by the ofticer is impaired. 

The "Cut-off." 

By a device which may limit the withdrawal of the bolt, 
the magazine may be 'Wut-ojf and its contents reserved for 
a suitable necessity. The piece meanwhile is used as a single 
louder. 

Such attachments are fragile and in moments of excitement 
are confusing. When tried under such circumstances, they 
have been found unsuited to the conditions of service. 

BOX MAGAZINES. 

By placing the cartridges side by side in a box, many of 
the objections urged against the tube disappear. The 
principal point to be decided relates to whether the box 
shall be detachable or fix 

1. Detachable Box- 

An example of this type is seen in the Lee magazine, 
figure 2, which consists of a box of sheet steel, in which the 
cartridges lie over the feed spring, N. 

The box is readily inserted through the mortise in the well 
of the receiver into the position shown. 

The operation of the bolt passes the cartridges in succes- 
sion into the chamber, and acts as a valve to regulate the 
ascent of those lemainmg to be fired. 

A number of these magazines are carried by the soldier, 
who IS expected to use his arm as a single loader until he 
receives the order to fix magazines. 



12 XXVIII. SMALL ARMS. 

This facilitates control by the officer, but the uncertainty 
of the soldier as to the state of the supply may lead him to 
go through the motions of firing with an empty arm. 

The principal objection to the system applies to the ex- 
cessive weight and cost of the box as a package, if many 
magazines are carried; and, if but few, to the probabiHty of 
losing so important a component in the act of replacing it 
under fire. 

2. Fixed Box. 

I. A prominent arm of this type is the Austrian Mannlicher 
rifle, figure 4. 

The cartridges are held by their bases in a sheet metal 
frame, the whole package being bodily inserted into the 
magazine through the well of the receiver, where it is retained 
by a spring latch, r, A follower^ /, impelled by a strong 
spring, ^, lifts the column so that the top cartridges are suc- 
cessively shoved into the chamber by the bolt. The fall of 
the empty case through the bottom of the magazine warns 
the soldier that the magazine is exhausted. 

In a recent model the heads of the cartridges are so held 
by the frame that they lie in the same plane. With this 
model no special care is needed in inserting the frame into 
the magazine; while in that shown, the obliquity of the frame, 
caused by the step-like arrangement of the heads, may cause 
confusion. 

The device for locking the arm consists of a brace, b^ 
attached to the bolt. It is forced downward in front of a 
shoulder, t", in the receiver, by a wedge-shaped projection 
below an axial stem to which the knob, k^ is attached. By 
simply pulling on the knob, the brace is lifted from its seat 
by the wedge, and the brace, knob and bolt slide out together. 

This arrangement avoids the rotation of the bolt required 
in the Lee and in almost every other bolt gun. 



XXVIII. — SMALL ARMS. 13 

This arm cannot be used as a single loader. 

2\ The Schulhojf magazine rifle, figure 5, may be used as 
such or as a single loader. 

The cartridges are carried in an annular box, beneath the 
receiver. 

The axial shaft, s, carries a radial plate, ox follower, f, that 
ia turned m one direction by the act of opening the lid, /, 
figure 6, and m the other direction by a spiral spring (not 
shown) surrounding the shatt, which is twisted in the act of 
opening. 

The cartridges may be thrown in loosely, or may be loaded 
in mass from the quick loader shown in figure 7. 

A circumferential slide, <:, operated by the thumb piece /, 
forms a very simple cut-off. 

The strength and solidity of the magazine enables it to be 
slit, so that the state of the supply may be seen at a glance. 

The position of the box enables it to be filled without 
unloading the arm. 

Quick Loader. 

A cheap quick loader, figure 7, containing the supply of 
cartridges for one magazine enables them to be transferred 
to it in mass when rapid recharging is required. For this 
purpose the lower end of the quick loader being placed over 
the mouth of the magazine the pressure of the thumb of the 
operator on top of the column of cartridges forces them 
down into the magazine against the resistance of the 
magazine spring. 

They are retained by a valve at the mouth of the magazine, 
and the quick loader is then thrown away. The valve serves 
to retain successive cartridges singly loaded. 
Form Proposed. 

The eventual preference of the fixed or the detachable 
box magazine will probably be largely determined by moral 
considerations. 



14 I XXVIII. SMALL ARMS. 

The dispersed formations of future wars will probably 
require a more extended exercise of discretion in the lower 
grades than has hitherto been customary. The question 
arises, how far down will the discretionary control of fire 
extend ? 

It is now proposed to attach the box magazine perma- 
nently to the receiver, and ordinarily to load the arm con- 
tinuously through the magazine, so that the cartridge last 
inserted shall be the first to be fired and that the number 
remaining shall be automatically held in reserve. 

It is possible that the time gained by making the opera- 
tion of the piece simple and invariable, as in the type pro- 
posed, may be so utilized in the general instruction of the 
troops that it will not be considered necessary to burden 
them with an inferior weapon in order to control their fire. 

REQUISITES OF A MAGAZINE ARM. 

The preceding considerations enable us to name the fol- 
lowing necessities : 

1. The best ballistic conditions attainable. These may 
modify the size and proportions of the cartridges, and so 
affect the capacity of the magazine. 

2. Consecutive rapidity of fire as a single loader as great 
as that of any other arm, and the greatest possible inter- 
mittent rapidity when the magazine is employed. 

3. The possibility of filling the magazine with single car- 
tridges, or " in mass," without unloading the piece. 

4. A maximum capacity which is yet to be determined 
by experience. It will probably be about 5 shots in the 
magazine. 

5. A ready view of the state of the supply. 

6. The most simple construction compatible with the 
maximum efficiency under the conditions of service. 

Beyond a certain point objections to complexity become 



Xxviii. — Small arms. 18 



pedantic, since experience shows that the instinct of self- 
preservation may be counted on for the care necessary to 
maintain an efficient arm. 

THE SPRINGFIELD RIFLE. 

History. 

This arm, although originally intended as a means of 
utilizing the large supply of muzzle loading muskets left by 
the Civil War, has acquired a standing which, in 1886, 
caused its preference by 73 per cent of the officers to whom 
were submitted, for comparative trial in service, three of the 
best magazine arms. 

Apart from the excellence of its manufacture and the ease 
with which it may be operated with but one hand, this pre- 
ference may be attributed to the independent action of a 
form of lock, the outgrowth of centuries of experience ; and 
the perfection of the apparatus for extraction and ejection. 

The design of the cam latch and of the firing pin are 
exposed to criticism. 

As a reserve supply of this arm is likely to be retained for 
many years after the adoption of a magazine gun, a few of 
its principles are described. The nomenclature is supposed 
to be known. 

Operation. Figure 8. 

Locking. 

When the piece is fired the tendency of the block to swing 
upward out of the receiver, A^ is corrected by the loose fit 
of the hinge pin, E^ in its hole. The block, therefore, sHdes 
bodily to the~rear until stopped by the interposition of the 
body of the cam latch F, between the block and the breech 
screw, C. The journals of the cam latch are loose in their 
bearings so that they may be free from strain. 

The centre of pressure on the breech screw is brought 



16 XXVIII. — SMALL ARMS. 

as nearly as possible in the prolongation of the axis of 
the bore so as to diminish the tangential component of the 
pressure, which tends to revolve the cam latch and tlirow 
open the block. This is imperfectly resisted by the friction 
developed by the normal pressure between the surfaces in 
contact, and also by the combined action of the thumb piece 
and the hammer, the functions of which are thereby perverted. 

Extraction. 
The power needed for extraction results from the compound 
lever formed by the breech block and the extractor, J, 

Ejection. 

In opening the block the revolution of the extractor com- 
presses the coiled ejector spring, K, until the action line of 
this spring passes from above the axis of rotation to below it. 

The expansion of the spring then rapidly revolves the ex- 
tractor. This impels the cartridge case against the ejector 
stud Z, which deflects it upward and throws it clear of the gun. 

Firing Mechanism. 

The lock, figures 9, 10, 11, consists of the lock plate, to 
which the parts are attached and by which the mechanism is 
secured to the stock by the side screws. 

The hammer, A^ outside the lock plate, and the tumbler, B^ 
inside of it form mechanically but one piece, the arrangement 
adopted being required for the protection of mechanism from 
dirt. 

The tumbler, B, is connected with the mainspring by a 
swivel, y, so disposed that the resistance to cocking the piece 
shall be nearly constant. This is accomplished by the varia- 
tion in the lever arm of the mainspring ; as the resistance of 
the mainspring due to its compression increases, the action 
line of the resistance passes nearer to the axis of the tumbler, 



kXVlIt. — SMALL ARMS. 17 

while the lever arm of the power, the thumb, is constant. 
The tumbler is thrice notched to receive the nose of the sear, 
E. This, under the action of the sear spring, G^ maintains 
the hammer at the distances from the head of the firing pin 
required for convenience of transportation, safety of loading, 
and certainty of fire, respectively. 

The bridle, C, holds the parts together. 

The oblique blow of the firing pin is objectionable. Chap- 
ter XXVII, page 5. 

RECENT DEVELOPMENT OF SMALL ARMS. 

PHYSICAL CONSTANTS. 

Owing to the mechanical improvements in the construction 
of arms and ammunition the ballistic development of the small 
arm is now limited by the soldier's endurance of its recoil. 
Similarly its tactical employment is limited by his ability to 
transport the burden of its ammunition ; for the maintenance 
of the rapid fire of the extended lines now rendered possible 
is a problem which increases in difficulty as the fire increases 
in rapidity and range. 

L Recoil. 

These constants are influenced by racial peculiarities, and 
may be considerably modified by training ; but the proper 
training of large armies in the endurance of recoil implies so 
great a cost, that the present tendency is to render the recoil 
supportable by inexperienced troops, so that the accuracy of 
their fire may not be impaired by their apprehension of its 
effects.* 



*Tlie effect of racial peculiarities, and incidentally of training, is shown 
by the following data which relate to arms of caliber about 0.45 in. 

In the relatively small armies of Great Britain and the U. S. the energy 
of recoil IS about 14 ft. pounds. 

The low average stature of the French fixes a limit of about 11 ft. 



18 XXVIII. — SMALL ARMS. 

2. Burden. 

Training in weight-carrying is not expensive, and its im- 
portance is becoming recognized by the frequency with which 
practice marches are made. As in the artillery service 
Chapter XXIV, page 2, a judicious distribution of the bur- 
den between the arm and its ammunition depends greatly 
upon the former's recoil. 

MODIFICATIONS OF THE RECOIL. 

The recoil may be reduced by modifying the arm or the 
ammunition. 

1. Modifications in the Arm. 

If the ballistic conditions are kept constant, the weight of 
the arm may be reduced, and a greater number of cartridges 
be carried, by : — 
, 1. The use of an elastic cushion attached either to the gun 
or to the clothing. 

These plans are found impracticable. 

2. Increasing the mass of the gun in firing by adding to it 
that of a portion of the ammunition, as in magazine guns. 

The correction is variable and sometimes injurious to 
accuracy. 

3. Storing up the energy of recoil as by the compression of 
a spring, which, by its resihence may operate the piece. 



pounds. But in Germany, although the ballistic conditions are nearly 
identical with the French, the desire for durability has developed the 
heaviest small arm known. Notwithstanding the strength of the Ger- 
mans the recoil is only 10 ft. pounds. 

In Italy, as in our service during the Civil War, about 7 ft. pounds is 
allowed. 

This IS the limit reached by the present reduction in caliber. The re- 
turn to the former standard, page 23, is significant of its practical con- 
stancy. 



XXVIII. — SMALL ARMS. 19 

This has been tried, but so far without success, owing to the 
complicated nature of the mechanism required. 

4. The pressure due to the recoil may be distributed over 
an increased area of the person by the proper use of the gun 
sling. By lying down to fire, the path of the recoil is 
shortened and the pressure on the body increased. 

General consent seems to have established the weight of 
the rifle at between 8.5 and 9.5 pounds. 

2. Modifications in the Ammunition. 

1. Caliber and Recoil Constant, 

The advantages of any particular cahber being general, 
that of all military rifles at any epoch is approximately con- 
stant. It has recently been about 0.45 inch. See figure 12. 

When the caliber and the weight of the arm are constant, 

the recoil can be reduced only at the expense of the ballistic 

properties of the arm. But these being maintained at the 

highest value consistent with the recoil endurable in any 

i 7n v V 
particular case, the Equation M E ■=. C ^ - — - — - shows 

that modifications in the ammunition must be confined to 
factoring the momentum of the projectile. The following 
considerations illustrate the effect of variations in m and z', 
their product in any one case being constant. 

a. If we increase w at the expense of z/, we lose in danger- 
ous space at short and decisive ranges but conversely at long 
distances. Chapter XX, page 40. 

b. During the wars of 1870 and 1877 it was found advis- 
able to deliver at extreme ranges an almost vertical fire 
against masses of troops. 

It has since been found that the extreme range increases 
more rapidly with the sectional density of the bullet than 
with its initial velocity. The present U. S. bullet was accord- 



20 XXVIII. — SMALL ARMS. 

ingly increased in weight from 405 to 500 grains, and an 
extreme range of two miles was attained. 

c. It is found that the accuracy of fire at moderate known 
distances is incompatible with tlie high velocities required in 
actual service. This is probably due to the vibration of the 
barrel. Page 4. 

Conclusion. 

Owing to the impossibility of simultaneously satisfying the 
requirements of the different ranges, it is considered that 
efficiency at long ranges should be sought by the use of special 
means, such as machine guns firing heavy projectiles. For 
small arms it is considered that accuracy should become sub- 
ordmate to flatness of trajectory for ranges exceeding 600 
yards, at which individuals cease to be distinguished by the 
unaided eye ; and that the trajectory should be so flat that 
but one height of the rear sight would be required within that 
distance, and the smallest number of changes beyond it. 

Differences of elevation within the limits of graduation 
would be adjusted by varying the coarseness of the front 
sight. Chapter XXX, page 2. 

2. Caliber Variable. 
These conditions can be attained, and the number of cart- 
ridges in a given burden increased, by reducing the caliber. 
Under the conditions named on page 2, the limit of reduc- 
tion has been fixed by the difficulties of manufacture and by 
those relating to the cleaning of the bore. 

Small Caliber Rifle. 

The following general principles govern the changes in 
ammunition resulting from the reduction in caliber. For 
simpHcity of treatment we will first assume the muzzle velocity 
unchanged from the larger caliber. 

Bullet, The sectional density, and therefore the length of 



XXVIII. — SMALL ARMS. 21 



the bullet, has remained approximately constant ; since, as 
shown in Chapter XVI, page 4, an increase in the sectional 
density would increase the value of /„, unless the muzzle 
velocity were reduced. 

The strength of the barrel is not materially greater than 
that of the caliber 0.45, and, owing to the reduction in the 
area corresponding to the bottom of the bore, the increase 
in the strength of the fermeture is only relative ; therefore, 
the maximum value of p^ formerly allowed cannot be greatly 
exceeded. 

The sectional density being constant, the reduction in 
caliber reduces the mass of the bullet, and therefore, although 
the ballistic properties of the arm (being dependent only 
upon the sectional density or C, Chapter XX, and the muzzle 
velocity) would not be affected, the recoil would be reduced 

(m' \ "^ 
— ). With the weights of bullet given in the 

following table, this would reduce the recoil from about 14 
foot-pounds to about 3 foot-pounds. 

Powder, This reduction being excessive, the normal 
endurance of the soldier against recoil is utilized by increas- 
ing the weight of the charge, and therefore the muzzle 
velocity. 

The baUistic properties of the arm are therefore improved, 
figure 12, but the internal pressure* would be excessive unless 



* If in Equation (D), Chapter XII, we place K^a^ /\=z C, and repre- 

IV , . w 

sent by (J = -jj the sectional density of the projectile, and by « = — 

the ratio between the weight of the powder and that of the projectile, we 
have, after reduction. 

But if, as in the case considered, 6 is constant, /„ will vary with nj^. 

From this it follows that if the same charge of the same kind of powder 
were used in the Hebler rifle as in the Springfield, the pressure would be 
nearly doubled. 



22 XXVIII. — SMALL ARMS. 



the powder were made specially progressive. The value of 

J for the cartridge shown in figure 14 is 11.43. See Table I, 

Chapter XII. 

In spite of these precautions the main difficulty in the new 
small caliber high-powered guns is due to the excessive pres- 
sures developed. 

Powder. 

The principal difficulties found in realizing the advantages 
of a reduction in caliber exist in the powder. 

It was thought by Professor Hebler, of Germany, to whom 
much of the credit of the proposed change is due, that these 
difficulties could be overcome by compressing the powder as 
in a rocket, in a cartridge case like the Morse. Figs. 13, 14. 

The objections to this method noted, Chapters XII, page 

21 ; XVI, page 45, and the large volume of smoke resulting 

from rapid fire, cause many to prefer a high explosive, such 

as described, Chapter XIV, page 15 ; in spite of its recognized 

objections. The complete solution of the problem is still 

deferred. 

Projectile, 

The projectile proposed is distinguished by its penetration, 
its cleanliness as regards the bore, and the nature of the 
wounds which it inflicts, page 2. When they are flesh wounds 
they are punctured rather than lacerated; but when they 
involve the bones these are shattered. 

Cartridge Case. 

In order to avoid the increase in the length and weight 
of the breech mechanism, resulting from the relative increase 
in the length of the cartridge case, this is made bottle-shaped, 
as in figure 14. 

This unfits it for reloading with compressed powder, unless 
the Morse cartridge be used ; the latter has been found too 
delicate to endure reloading by troops. 



XXVIII. — SMALL ARMS. SS 

In some cases the volume of the magazine has been 
diminished by eliminating the rim and replacing it by a V 
shaped groove, in which the hook of the extractor may 
engage, figure 16. In order to faciUtate reloading with per- 
forated cyhnders of powder, previously compressed, such as 
c, the cavity is cylindrical ; the reduction in diameter being 
made by a brass ring, r. The blow of the hammer is sup- 
ported by XhQ front of the cartridge case. 

Comparison. 

The following table illustrates the advantages of the 
reduced cahber, since it compares the present Springfield 
rifle, which is one of the best of the arms recently used, 
with the Hebler, which is a fair type of the arms proposed : 





Springfleld. 


Hebler. 


Caliber, inches 


0.450 


0.296 


Bullet, wt. grains, 


500 


225 


Powder, wt. grains. 


70 


83 


Sectional density, 


0.353 


0.367 


Spherical density. 


3.6 


5.6 


Twist in inches, 


22 


4.58 


Twist in calibers, ratio about, 


3 


1 


Initial velocity, f. s., 


1280 


1942 


Cartridges, ratio of weights, 


100 


85. 


Arm, weights pounds. 


9.3 


9.9 


Maximum dangerous space, yds.. 


880 


440 


Accuracy at 440 yds., ratio 


1 


3 


Muzzle energy, foot-pounds. 


1818 


1882 


Recoil energy, foot-pounds. 


13.95 


6.11 



REVOLVERS, 

As a military weapon the revolver is useful principally in 
enabling a horseman to use but one hand in delivering a 
rapid fire. In closed masses its employment is dangerous, 



24 XXVlll. — SMALL ARMS. 

since it is difficult to fire to the front without striking the 
horse or the leading files, and the shortness of. the piece 
leads to accidents to those alongside. 

It is therefore considered generally an inferior arm, and one 
to be used only for personal defence and in maintaining dis- 
cipline upon the field. Its ballistic properties need not be 
greater than necessary to stop a man at 50 or 60 yards. 

The revolver is one of the oldest forms of magazine arms. 
Its present perfection is due to the invention of Col. Colt of 
Hartford, who combined the cocking of the hammer with 
the revolution of the cylinder. 

Owing to the considerable moment of inertia of the loaded 
cylinder, this tends when rapidly revolved to pass the position 
in which the axis of the chamber next to be fired coincides 
with that of the barrel. This is the principal difficulty found 
in the construction of these arms. 

To facihtate their operation, revolvers are sometimes made. 
self'Cockifig, the action of the trigger causing all the motions 
to be performed. For greater continuous rapidity of fire, in 
which these arms, like many magazine rifles, are deficient, 
the cartridges may be simultaneously extracted by sliding or 
swinging the barrel and cylinder away from the breech. The 
chambers may then be simultaneously reloaded by using 
ammunition packed in clusters. 

The complexity of these refinements and the limited scope 
of the revolver generally cause simpler patterns to be pre- 
ferred. 

MANUPACTURE OF SMALL ARMS. 

Where Made. 

The service rifle and carbine are made by the Ordnance 
Department at the National Armory. Pistols and such other 
special arms as may from time to time be needed are bought 
from private estabUshments. 



XXVIII. — SMALL ARMS. 25 

How Made. 

Efficiency in service and ultimate economy in manufacture 
require that the similar parts of arms of the same model shall 
be interchangeable. This is secured by the principle of 
gauging, noted in Chapters IV and XVII. 

Gauging. 

The general design of a gun having been perfected, an 
exact working model is carefully prepared. The component 
parts are so formed as to be as far as possible adapted to the 
operation of the varieties of the lathe. Chapter XVII, 
page 13. 

Each of the components is then examined with reference 
to its gauging points. These are the surfaces between which 
the most exact relations are required. 

For surfaces of revolution like the barrel, or parts intended 
to revolve like the Springfield breech block and the tumbler, 
the gauging points are established with reference to the axis 
of rotation. 

For pieces subject to compression, like the bolt of the Lee 
rifle, the greatest pains would be taken with the distance from 
the rear face of the locking mass, a', to the front face of the 
bolt ; and, in the receiver, with the distance from the shoulder, 
a, to the plane containing the mouth of the chamber, since 
the difference of these distance must be kept invariable in 
order to insure the proper working of the ammunition. 

While the first of these is readily gauged, the second in- 
volves the relations between the barrel and the receiver ; 
each of which must be similarly watched with reference to 
their abutting surfaces. 

When the number of such surfaces is considerable, as in 
the Springfield mechanism, the sum of their possible errors 
requires the closest gauging of each link of the chain of parts. 

Many forms of gauges are employed. They may be 



26 XXVIII. — SMALL ARMS. 

classified like patterns as positive or negative gauges, the 
latter being sometimes simple notches, and sometimes mat- 
rices so formed as to contain exactly pieces of an irregular 
shape. 

To retard their wear, the working surfaces of gauges are 
made of hardened steel ; and, as steel tends in hardening 
to change its form, these surfaces are finished in the hardened 
state. 

The number of gauges required not only for the finished 
parts but for the intermediate stages demand that, before the 
first arm of a series be produced, many thousand dollars shall 
be expended in preparation. 

When tlie gauges and the corresponding tools and fixtures 
are made, the work goes on rapidly ; for the functions of each 
workman are independent, and no time is wasted in fitting 
the product of different hands. 

In illustration: The model may cost $600 — the first hun- 
dred guns made from the gauges $100 each, and the first ten 
thousand, all equal in quality to the model, $15 each. 

The sense of feeling is so much more acute than that of 
sight, that by the use of guages differences far within the 
limits of ordinary measurement may be detected. The thou- 
sandth part of an inch is the customary unit, and this may 
be subdivided practically according to the requirements of 
the work. 

The system more than anything else promotes the "division 
of labor," upon which industrial prosperity depends ; and, by 
substituting an absolute for a discretionary standard, it edu- 
cates in a remarkable manner the workman upon whose skill 
the value of the product is practically based. 

OPERATIONS OF MANUFACTURE, 

Barrels. 

The principal operations are rolling, boring, turning, 
straightening and rifling. The rolling is done as previously 



XXVIII. — SMALL ARMS. 27 

described, Chapter XV, page 44. While hot the rough ends 
of the tube are sawed off and it is straightened under a drop 
hammer, after which it is annealed by the residual heat. 
When cold the hard scale is removed by pickling in diluted 
acid. 

In the preliminary borings the revolving auger is drawn 
through the barrel instead of being pushed, so as to keep the 
hole straight.* The bore is then enlarged by rapidly re- 
volving reamers whose cross sections are square. 

In turnhig the slide rest is guided by a template so as to 
produce a conical surface, and the barrel is kept from 
springing by the back rest. 

Straightenifig is performed by light blows of the hand 
hammer appHed at points which are indicated by the shadow 
of a straight edge reflected from the walls of the bore. This 
operation requires a peculiar knack which very few can 
acquire. 

In order to secure uniformity in the rifling^ a number of 
cutters equal to that of the grooves is provided and these 
are transferred automatically between adjoining grooves at 
the end of each stroke of the axial rifling rod. 

This rod receives a combined motion of translation and 
rotation, by which, as in rifled cannon, the spiral motion is 
produced. 

While in an intermediate stage, the barrel is proved by fir- 
ing a very large charge of both powder and lead. 

The final proof of the efficiency of the mechanism and 
of the accuracy of the arm is made with service ammunition. 

MANUFACTURE OF THE MINOR PARTS. » 

The form is defined roughly by Gorging between dies. 



*The adoption of the 0.30 caliber will increase the difficulty of boring 
since the barrel may require to be rolled solid and bored under 
compression. 



28 XXVIII. — SMALL ARMS. 

The slow operation of a very powerful press permits many 
parts to be reduced to nearly their finished dimensions 
when cold. 

The principles of milling, Chapter XVII, are used when- 
ever practicable. The most complicated arms have thus 
been made without requiring the use of the file. 

The most interesting operations are those required to pro- 
duce irregular forms. 

Profiling. 

The profiler is a sort of milling machine in which relative 
motion in three coordinate directions can be produced between 
the revolving mill and the work. To limit the relative dis- 
placements the following arrangement is provided. See 
figure 17. 

To a table moving in a horizontal plane the work, W, is 
clamped at a fixed distance from a hardened steel model, M, 
of the finished part. 

At the same distance from the mill, m, and with its axis 
vertical, is a blank pin, /, of corresponding dimensions. We 
thus have two pairs of parts ; one pair consistmg of the 
model and the work and the other of the pin and the mill, 
with relative motion between the pairs. When the mill begins 
to cut it is necessary only to cause the pin to follow the pro- 
file of the model in order to reproduce it in the work. 

The intricate l^ed or matrix of the lock is thus formed with 
the greatest accuracy in about one mmute. 

Eccentric Turning. 

This operation was devised by Thomas Blanchard, an em- 
ployee of the National Armory, for the purpose of forming 
the gun stock. It has been applied to many other useful 
purposes, as in the manufacture of shoe lasts, spokes, and 
even of statuary. Its principle is as follows: See figure 18. 

In ordinary turning the cutter does not sensibly change its 



XXVIII. — SMALL ARMS. 29 

distance from the axis during one revolution of the work and 
therefore leaves behind it a partically concentric surface. 

But in eccentric turning the cutter, C, which revolves after 
the manner of a mill about an independent axis parallel to that 
of the work, is caused to oscillate slowly in a plane normal 
to the axis of rotation during each revolution of the work, JV. 
This oscillation is produced by an iron model, J/, revolving 
with and parallel to the work and resting against a blank 
wheel, B, attached to the oscillating frame which supports 
the cutter. 

In concentric turning the cutting speed is due to the tan- 
gential velocity of the work, and in eccentric turning the 
high speed required in wood working is due to that of the 
cutter. The motion of translation is similarly performed in 
both cases. 

The cutting edges are placed at progressively increasing 
radial distances, so as to cut to different depths during each 
revolution of the cutter. This principle is frequently applied 
in revolving tools. 

The developed length of the cuts required to turn a gun- 
stock is 13 miles ; the operation takes about 8 minutes. 

Blacking and Browning. 

To protect the parts from rust and to prevent them from 
flashing in the sun, small pieces are blackened by heating 
them until they will ignite the oil with which they are covered. 

The outside of the barrel is oxidized by coating it with a 
dilute acid mixture and exposing it in a warm, damp place. 
The loose coating of red oxide having been brushed off, a 
permanent layer of black rust remains. Some parts are 
rapidly oxidized by immersing them in fused nitre. 



XXIX. — CANNON WITHOUT RECOIL. 



CHAPTER XXIX. 

CANNON WITHOUT RECOIL. 

The advantages of rapid fire from cannon would be 
neutralized by the time required to readjust